The conference brochure - University of Nevada, Las Vegas

Transcription

THE EIGHTH INTERNATIONAL CONFERENCE ON
SCIENTIFIC COMPUTING AND APPLICATIONS
University of Nevada, Las Vegas
April 1 – 4, 2012
Program and Abstracts
Department of Mathematical Sciences, University of Nevada, Las Vegas
Sponsors
National Science Foundation
USA
National Security Technologies
LLC, USA
Table of Contents
Committees
1
Plenary Speakers
2
Schedule
3
Program
Sunday, April 1, 2012 . . .
Monday, April 2, 2012 . .
Tuesday, April 3, 2012 . .
Wednesday, April 4, 2012
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
Abstracts
Plenary Talks . . . . . . . . . . . . . . .
Walter Allegretto’s 70th Birthday . .
Graeme Fairweather’s 70th Birthday
Mini-symposia . . . . . . . . . . . . . .
Other Talks . . . . . . . . . . . . . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
7
7
13
19
26
.
.
.
.
.
29
29
35
38
42
69
List of Participants
87
CBC and Hyatt Place
92
UNLV Campus Map
93
Committees
Scientific Committee
Randolph Bank, University of California - San Diego, USA
Gang Bao, Michigan State University, USA
Russ Caflisch, University of California - Los Angeles, USA
Zhangxing (John) Chen, University of Calgary, Canada
Graeme Fairweather, American Mathematical Society, USA
Max Gunzburger, Florida State University, USA
Jan Hesthaven, Brown University, USA
Yunqing Huang, Xiangtan University, China
Youssuff Hussaini, Florida State University, USA
Jin-Fa Lee, Ohio State University, USA
Yanping Lin, The Hong Kong Polytechnic University, Hong Kong
Chi-Wang Shu, Brown University, USA
Tao Tang, The Hong Kong Baptist University, Hong Kong
Ren-hong Wang, Dalian University of Technology, China
Mary Wheeler, University of Texas at Austin, USA
Yau Shu Wong, University of Alberta, Canada
Organizing Committee
Yitung Chen, University of Nevada, Las Vegas, USA
Derrick Dubose, University of Nevada, Las Vegas, USA
Jichun Li (Co-Chair), University of Nevada, Las Vegas, USA
Eric Machorro, National Security Technologies, LLC, USA
Monika Neda, University of Nevada, Las Vegas, USA
Pengtao Sun, University of Nevada, Las Vegas, USA
Hongtao Yang (Co-Chair), University of Nevada, Las Vegas, USA
1
Plenary Speakers
Todd Arbogast, University of Texas at Austin, USA
Randolph Bank, University of California - San Diego, USA
Gang Bao, Michigan State University, USA
Pavel Bochev, Sandia National Lab, USA
Zhangxing (John) Chen, University of Calgary, Canada
Leszek Demkowicz, University of Texas at Austin, USA
Jan Hesthaven, Brown University, USA
Yunqing Huang, Xiangtan University, China
Mary Wheeler, University of Texas at Austin, USA
Jinchao Xu, Pennsylvania State University, USA
Zhimin Zhang, Wayne State University, USA
2
3
Concurrent Sessions
4:30 PM – 5:00 PM
5:00 PM – 5:30 PM
5:30 PM – 6:00 PM
Concurrent Sessions
3:00 PM – 3:30 PM
3:30 PM – 4:00 PM
4:00 PM – 4:30 PM
Concurrent Sessions
10:00 AM – 10:30 AM
10:30 AM – 11:00 AM
11:00 AM – 11:30 AM
11:20 AM – 12:00 PM
12:00 PM – 2:00 PM
2:00 PM – 2:50 PM
Plenary Talks
8:00 AM – 8:30 AM
8:40 AM – 9:30 AM
Plenary Talks
9:30 AM – 10:00 AM
Sunday, April 1, 2012
CBC A
Registration
CBC A106
Mary Wheeler (Chair: I. Yotov)
CBC A110
Jan Hesthaven (Chair: Jichun Li)
Coffee Break
CBC C116
CBC A110
CBC A106
MS4: Yanzhi Zhang Chair: Jan Hesthaven SS for Allegretto
Peijun Li
Aihua Wood
Openning Remarks
Maojun Li
Vrushali Bokil
Chiara Mocenni
Nghiem V. Nguyen Shaozhong Deng
Shuhua Zhang
Yanzhi Zhang
Peijun Li
Peter Minev
Lunch at Hazel M. Wilson Dining Commons (DIN)
CBC A106
Max Gunzburger (Chair: Hongao Yang)
CBC A110
Jinchao Xu (Chair: Pengtao Sun)
CBC C116
CBC A110
CBC A106
MS8: Barth et al.
Chair: Jinchao Xu
SP for Allegretto
Mats Larson
Ranis Ibragimov
Duccio Papini
Paul Houston
Grace F. Jefferson
Liqun Cao
Coffee Break
CBC C116
CBC A110
CBC A106
MS8: Barth et al.
MS2: Chen/Ringler
SP for Allegretto
Lukas Korous
Antoine Rousseau
Jiang Zhu
Pavel Solin
Leslie Smith
Kai Huang
August Johansson
Mark Taylor
Raymond Chan
CBC C118
MS9: Kachroo/Machorro
Neveen Shlayan
Daniele Schiavazzi
Lillian Ratliff
CBC C118
MS6: Sun/Chen/Hu
Long Chen
Pengtao Sun
CBC C118
MS9: Kachroo/Machorro
Jerome Blair
P.D. Spanos
Aaron Luttman
A.V. Balakkrishnan
Schedule
Schedule
8:30 AM – 9:20 AM
Plenary Talks
Concurrent Sessions
9:30 AM – 10:00 AM
10:00 AM – 10:30 AM
10:30 AM – 11:00 AM
Concurrent Sessions
11:00 AM – 11:30 AM
11:30 AM – 12:00 PM
12:00 PM – 12:30 PM
12:30 PM – 2:00 PM
2:00 PM – 2:50 PM
Plenary Talks
Concurrent Sessions
3:00 PM – 3:30 PM
3:30 PM – 4:00 PM
4:00 PM – 4:30 PM
Concurrent Sessions
4:30 PM – 5:00 PM
5:00 PM – 5:30 PM
5:30 PM – 6:00 PM
6:30 PM – 9:30 PM
Monday, April 2, 2012
CBC A106
Zhimin Zhang (Chair: Chi-Wang Shu)
CBC A112
Zhangxing Chen (Chair: M. Neda)
CBC A106
CBC C116
CBC A112
CBC C118
Chair: Zhimin Zhang
Chair: W. Layton
SS for Fairweather Chair: Shangyou Zhang
Weimin Han
Jue Yan
B. Bialecki
Qi Wang
Sum Chow
Jianxian Qiu
Xiao-Chuan Cai
Chuanju Xu
Coffee Break
CBC C116
CBC C118
CBC A112
CBC A106
MS8: Barth...
Chair: A. Wood
SS for Fairweather MS7: Sun/Li
Jeff Banks
Zhen Peng
R.I. Fernandes
Erkki Somersalo
Tim Barth
Min Hyung Cho
Raymond Chan
Ying He
Murtazo Nazarov
Shan Zhao
Michael McCourt
Xia Ji
CBC A106
Chi-Wang Shu (Chair: Max Gunzburger)
CBC A112
Graeme Fairweather (Chair: Mary Wheeler)
CBC C116
CBC C118
CBC A112
CBC A106
MS1: Zhangxing Chen MS5: Neda/Manica SS for Fairweather Chair: Weimin Han
Shuyu Sun
Daniela Calvetti
Paul Muir
NCLab: Pavel Solin
E.W. Jenkins
Traian Iliescu
C.S. Chen
NCLab: Pavel Solin
Coffee Break
CBC C116
CBC C118
CBC A112
CBC A106
MS1: Zhangxing Chen MS5: Neda/Manica SS for Fairweather MS7: Sun/Li
Guangri Xue
William Layton
Weiwei Sun
Jiguang Sun
Wenyuan Liao
Maxim Olshanskii
A. Karageorghis
T.R. Khan
Xiaofeng Yang
Qin Sheng
Banquet at Richard Tam Alumni Center (TAC)
4
5
Concurrent Sessions
4:30 PM – 5:00 PM
5:00 PM – 5:30 PM
5:30 PM – 6:00 PM
Concurrent Sessions
3:00 PM – 3:30 PM
3:30 PM – 4:00 PM
4:00 PM – 4:30 PM
Concurrent Sessions
11:00 AM – 11:30
11:30 AM – 12:00
12:00 PM – 12:30
12:30 PM – 2:00 PM
2:00 PM – 2:50 PM
Plenary Talks
Concurrent Sessions
9:30 AM – 10:00 AM
10:00 AM – 10:30 AM
10:30 AM – 11:00 AM
8:30 AM – 9:20 AM
Plenary Talks
CBC A106
Pavel Bochev (Chair: Gang Bao)
CBC A112
Leszek Demkowicz (Chair: Shuyu Sun)
CBC C116
CBC A106
CBC A112
MS3: Evans/Perego
Chair: Pavel Bochev MS6: Sun/Chen/Hu
Daniel Martin
Zhijian Wu
Ming Wang
Helene Seroussi
Jari A. Toivanen
Chensong Zhang
Coffee Break
CBC C116
CBC A106
CBC A112
MS3: Evans/Perego
MS2: Chen/Ringler MS6: Sun/Chen/Hu
Xylar Asay-Davis
Robert Higdon
Liuqiang Zhong
Carl Gladish
Ram Nair
Shanyou Scott Zhang
Guillaume Jouvet
Wei Leng
Yunrong Zhu
CBC A106
Gang Bao (Chair: Eric Machorro)
CBC A112
Todd Arbogast (Chair: Long Chen
CBC C116
CBC A106
CBC A112
MS3: Evans/Perego
MS5: Neda/Manica MS6: Sun/Chen/Hu
Tobin Isaac
Jason Howell
Xiaozhe Hu
Jed Brown
Alexander Labovsky Jun Hu
Coffee Break
CBC C116
CBC A106
CBC A112
Chair: Todd Arbogast MS5: Neda/Manica MS6: Sun/Chen/Hu
Diego Assêncio
Hyesuk Lee
Wing-Cheong (Jon) Lo
Matthew Hubbard
Carolina Manica
Xinfeng Liu
Xu Zhang
Monika Neda
Lili Ju
Tuesday, April 3, 2012
CBC C118
Chair: R.B. Kearfott
A. Warzyński
He Yang
Roberto Corcino
CBC C118
Chair: Pavel Solin
Cristina Corcino
Mike Dameron
CBC C118
Chair: Qi Wang
Zhiping Li
Ivan Yotov
Huoyuan Duan
CBC C118
Chair: Huoyuan Duan
R.B. Kearfott
Fatih Celiker
Schedule
Schedule
8:30 AM – 9:20 AM
Plenary Talks
Concurrent Sessions
9:300 AM – 10:00 AM
10:00 AM – 10:30 AM
10:30 AM – 11:00 AM
Concurrent Sessions
11:00 AM – 11:30 AM
11:30 AM – 12:00 PM
12:00 PM – 12:30 PM
12:30 PM – 2:00 PM
CBC A106
Randolph Bank (Chair: Yanping Lin)
CBC A112
Jichun Li (Chair: Yau Shu Wong)
CBC C116
CBC A106
CBC A112
Chair: Shuhua Zhang MS5: Neda/Manica MS6: Sun/Chen/Hu
Martin Stynes
Abigail Bowers
James Brannick
Tong Kang
Leo Rebholz
Jeffrey Ovall
Coffee Break
CBC C116
CBC A106
CBC A112
Chair: Martin Stynes MS5: Neda/Manica MS6: Sun/Chen/Hu
Yanping Chen
Hoang Tran
Hengguang Li
Todd Ringler
Nicholas Wilson
Hualong Feng
Dominik Schoetzau
Wenxiang Zhu
6
Program
8:00 AM – 8:30 AM: Registration at CBC A
8:40 AM – 9:30 AM: Two Concurrent Plenary Talks
Room: CBC A106
Chair: Ivan Yotov, University of Pittsburgh, USA
Coupling Compositional Flow, Transport, and Mechanics in Porous Media for
Modeling Carbon Sequestration in Saline Aquifers (p. 33)
Mary F. Wheeler, The University of Texas at Austin, USA
Room: CBC A110
Chair: Jichun Li, University of Nevada, Las Vegas, USA
Reduced Models You can Believe in (p. 32)
Jan S. Hesthaven, Brown University, USA
9:30 AM – 10:00 AM: Coffee Break
10:00 AM – 12:00 PM: Four Concurrent Sessions
Room: CBC C116
Mini-symposium 4
Advances in analytical and computational techniques for nonlinear waves
Organizer: Yanzhi Zhang, Missouri University of Science and Technology, USA
10:00 AM – 10:30 AM Analysis of electromagnetic cavity scattering problems (p. 50)
Peijun Li, Purdue University, USA
10:30 AM – 11:00 AM Central discontinuous Galerkin methods for shallow water waves
(p. 50)
Maojun Li, Rensselaer Polytechnic Institute, USA
7
11:00 AM – 11:30 AM
11:30 AM – 12:00 PM
Global existence for a system of Schrödinger equations with
power-type nonlinearities (p. 51)
Nghiem V. Nguyen, Utah State University, USA
Numerical methods for rotating dipolar BEC based on a rotating
Lagrange coordinate (p. 51)
Yanzhi Zhang, Missouri University of Science and Technology,
USA
Room: CBC A110
Chair: Jan Hesthaven, Brown University, USA
10:00 AM – 10:30 AM Topics on electromagnetic scattering from cavities (p. 77)
Aihua W. Wood, Air Force Institute of Technology, USA
10:30 AM – 11:00 AM High Order Finite Difference Methods for Maxwell’s Equations
in Dispersive Media (p. 69)
Vrushali Bokil, Oregon State University, USA
11:00 AM – 11:30 AM Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions
(p. 70)
Shaozhong Deng, UNC Charlotte, USA
11:30 AM – 12:00 PM Generalized Foldy-Lax Formulation and its Application to the
Inverse Scattering (p. 73)
Room: CBC A106
A Special Session in Honor of Walter Allegretto’s 70th Birthday
Chair: Hong Xie, Manulife Financial, Canada
10:00 AM – 10:30 AM Openning Remarks
10:30 AM – 11:00 AM Homogenization and parameter estimation of reaction-diffusion
systems with rough boundaries (p. 36)
Chiara Mocenni, University of Siena, Italy
11:00 AM – 11:30 AM A Front-fixing Finite Element Method for the Valuation of American Options with Regime Switching (p. 37)
Shuhua Zhang, Tianjin University of Finance and Economics,
China
11:30 AM – 12:00 PM A Direction Splitting Algorithm for Flow Problems in Complex/Moving Geometries (p. 35)
Peter Minev, University of Alberta, Edmonton, Canada
Room: CBC C118
Mini-symposium 9
Uncertainty Quantification For Signal Processing and Inverse Problems
Organizers: Pushkin Kachroo, University of Nevada, Las Vegas, USA
8
10:00 AM – 10:30 AM
Estimating the bias of local polynomial approximation methods
using the Peano kernel (p. 66)
Jerome Blair, Keystone International and NSTec, USA
10:30 AM – 11:00 AM Hybrid Numerical Techniques for Efficient Determination of
stochastic Nonlinear Dynamic Responses via harmonic Wavelets
(p. 67)
P.D. Spanos, Rice University, USA
11:00 AM – 11:30 AM Computational Methods for Analyzing Fluid Flow Dynamics
from Digital Imagery Authors (p. 67)
Aaron Luttman, National Security Technologies LLC, USA
11:30 AM – 12:00 PM Application of Random Field Theory (p. 67)
A.V. Balakkrishnan, University of California, Los Angeles,
USA
12:00 PM – 2:00 PM: Lunch at Hazel M. Wilson Dining Commons
2:00 PM – 2:50 PM: Two Concurrent Plenary Talks
Room: CBC A106
Chair: Hongtao Yang, University of Nevada, Las Vegas, USA
Efficient Numerical Approaches for the Simulation and Control of PDEs with
Random Inputs (p. 32)
Room: CBC A110
Chair: Pengtao Sun, University of Nevada, Las Vegas, USA
Optimal Discretization, Adaptation and Iterative Solver for High Order Partial
Differential Equations (p. 33)
Jinchao Xu, Penn State University, USA
3:00 PM – 4:00 PM: Four Concurrent Sessions
Room: CBC C116
Mini-symposium 8
Recent Developments in Adaptivity and A Posteriori Error Analysis
Organizers: Tim Barth, NASA, USA
Paul Houston, University of Nottingham, UK
Mats Larson, University of Umea, Sweden
9
3:00 PM – 3:30 PM
3:30 PM – 4:00 PM
Adaptive Model Reduction for Coupled Thermoelastic Problems
(p. 63)
Mats Larson, Umeå University, Sweden
Two-Grid hp–Adaptive Discontinuous Galerkin Finite Element
Methods for Second–Order Quasilinear Elliptic PDEs (p. 64)
Room: CBC A110
Chair: Jinchao Xu, Pennsylvania State University, USA
3:00 PM – 3:30 PM Lie Group Analysis – a microscope of physical and engineering
sciences (p. 80)
Ranis N. Ibragimov, University of Texas at Brownsville, USA
3:30 PM – 4:00 PM Higher and Approximate Symmetries of Differential Equations
Using MAPLE (p. 84)
Grace Jefferson, Deakin University, Australia
Room: CBC A106
Chair: Raymond Chan, The Chinese University of Hong Kong, Hong Kong
3:00 PM – 3:30 PM Periodic solutions to nonlinear equations with oblique boundary
conditions (p. 36)
Duccio Papini, Università degli Studi di Siena, Italy
3:30 PM – 4:00 PM A Molecular Dynamics-Continuum Coupled Model for Heat
Transfer in Composite Materials (p. 35)
Liqun Cao, Chinese Academy of Sciences, China
Room: CBC C118
Mini-symposium 6
Multilevel and Adaptive Methods for Solving Complex Systems
Organizers: Pengtao Sun, University of Nevada Las Vegas, USA
Long Chen, University of California, USA
Jun Hu, Peking University, China
3:00 PM – 3:30 PM A Robust and Efficient Method for Steady State Patterns in
Reaction-Diffusion Systems (p. 59)
Wing-Cheong (Jon) Lo, The Ohio State University, USA
3:30 PM – 4:00 PM Dirichlet/Robin iteration-by-subdomain Schwarz-DDM for multiphase fuel cell model with micro-porous layer (p. 60)
Pengtao Sun, University of Nevada Las Vegas, USA
4:00 PM – 4:30 PM: Coffee Break
10
4:30 – 6:00 PM: Four concurrent sessions
Room: CBC C116
Mini-symposium 8
4:30 PM – 5:00 PM Advanced Aspects of Adaptive Higher-Order Methods (p. 64)
Lukas Korous, Charles University, Prague
5:00 PM – 5:30 PM Adaptive Higher-Order Finite Element Methods for Transient
PDE Problems Based on Embedded Higher-Order Implicit
Runge-Kutta Methods (p. 65)
Pavel Solin, University of Nevada, Reno, USA
5:30 PM – 6:00 PM Blockwise Adaptivity for Time Dependent Problems Based on
Coarse Scale Adjoint Solutions (p. 65)
August Johansson, University of California, Berkeley, USA
Room: CBC A110
Mini-symposium 2
Insight Into Geophysical Fluid Dynamics Through Analysis and Computation
Organizers: Qingshan Chen and Todd Ringler, Los Alamos National Laboratory, USA
4:30 PM – 5:00 PM On the quasi-hydrostatic ocean models (p. 45)
Antoine Rousseau, INRIA, France
5:00 PM – 5:30 PM Tropical Cyclogenesis and Vertical Shear in a Moist Boussinesq
Model (p. 45)
Leslie Smith, University of Wisconsin, Madison, USA
5:30 PM – 6:00 PM A Spectral Element Method for the Community Atmosphere
Model (p. 46)
Mark Taylor, Sandia National Laboratory, USA
Room: CBC A106
Chair: Peter Minev, University of Alberta, Edmonton, Canada
4:30 PM – 5:00 PM Mixed finite element analysis of thermally coupled nonNewtonian flows (p. 37)
Jiang Zhu, Laboratório Nacional de Computação Cientı́fica,
Brazil
5:00 PM – 5:30 PM Instant System Availability (p. 71)
Kai Huang, Florida International University, USA
11
5:30 PM – 6:00 PM
A Variational Approach for Exact Histogram Specification (p. 35)
Raymond Chan, The Chinese University of Hong Kong, Hong
Kong
Room: CBC C118
Mini-symposium 9
4:30 PM – 5:00 PM Analysis and Methods for Time Resolved Neutron Detection
(p. 67)
Neveen Shlayan, Singapore-MIT Alliance for Research & Technology, MIT, USA
5:00 PM – 5:30 PM Stochastic Spectral Approximation with Redundant Multiresolution Dictionaries for Uncertainty Quantification (p. 68)
Daniele Schiavazzi, Stanford University, USA
5:30 PM – 6:00 PM Conservation Law Methods for Uncertainty Propagation in Dynamic Systems (p. 68)
Lillian Ratliff, UC Berkeley, USA
12
Program
8:30 AM – 9:20 AM: Two concurrent plenary talks
Room: CBC A106
Chair: Chi-Wang Shu, Brown University, USA
Unclaimed Territories of Superconvergence I: Spectral and Spectral Collocation
Methods (p. 34)
Room: CBC A112
Chair: Monika Neda, University of Nevada, Las Vegas, USA
Challenges in Numerical Simulation of Unconventional Oil and Gas Reservoirs
(p. 30)
Zhangxing Chen, University of Calgary, Canada
9:30 – 10:30: Four concurrent sessions
Room: CBC A106
Chair: Zhimin Zhang
9:30 AM – 10:00 AM
10:00 AM – 10:30 AM
On A Family of Models in X-ray Dark-field Tomography (p. 71)
Weimin Han, University of Iowa, USA
Multi-frequency methods for an inverse source problem (p. 69)
Sum Chow, Brigham Young University, USA
Room: CBC C116
Chair: William Layton, University of Pittsburgh, USA
9:30 AM – 10:00 AM Direct Discontinuous Galerkin method and Its Variations for Diffusion Problems (p. 78)
Jue Yan, Iowa State University, USA
13
10:00 AM – 10:30 AM
Hybrid weighted essentially non-oscillatory schemes with different indicators (p. 74)
Jianxian Qiu, Xiamen University, China
Room: CBC A112
A Special Session in Honor of Graeme Fairweather’s 70th Birthday
Chair: C.S. Chen, University of Southern Mississippi, USA
9:30 AM – 10:00 AM Orthogonal Spline Collocation for Quasilinear Parabolic Problems with Nonlocal Boundary Conditions (p. 38)
B. Bialecki∗ , Colorado School of Mines, USA
10:00 AM – 10:30 AM A Space-time Domain Decomposition Method for Stochastic
Parabolic Problems (p. 38)
Xiao-Chuan Cai, University of Colorado at Boulder, USA
Room: CBC C118
Chair: Shangyou Zhang, University of Delaware, USA
9:30 AM – 10:00 AM Multiphase complex fluid models and their applications to complex biological systems (p. 76)
Qi Wang, University of South Carolina, USA
10:00 AM – 10:30 AM Fractional Differential Equations: Modeling and Numerical Solutions (p. 78)
Chuanju Xu, Xiamen University, China
11:00 AM – 12:30 PM: Four concurrent sessions
Room: CBC C116
Mini-symposium 8
11:00 AM – 11:30 AM A Posteriori Error Estimation via Nonlinear Error Transport
(p. 65)
Jeff Banks, Lawrence Livermore National Laboratory, USA
11:30 AM – 12:00 PM Dual Problems in Error Estimation and Uncertainty Propagation
for Hyperbolic Problems (p. 65)
Tim Barth, NASA Ames Research Center Moffett Field, USA
14
12:00 PM – 12:30 PM
A Posteriori Error Estimation for Compressible Flows using Entropy Viscosity (p. 66)
Murtazo Nazarov, Texas A&M University, USA
Room: CBC C118
Chair: Aihua Wood, Air Force Institute of Technology, USA
11:00 AM – 11:30 AM A Scalable Non-Conformal Domain Decomposition Method For
Solving Time-Harmonic Maxwell Equations In 3D (p. 72)
Zhen Peng, Ohio State University, USA
11:30 AM – 12:00 PM A Fast Volume Integral Solver for 3-D Objects Embedded in Layered Media (p. 79)
Min Hyung Cho, The University of North Carolina at Charlotte, USA
12:00 PM – 12:30 PM High order interface methods for electromagnetic systems in dispersive inhomogeneous media (p. 78)
Shan Zhao, University of Alabama, USA
Room: CBC A112
Chair: Andreas Karageorghis, University of Cyprus, Cyprus
11:00 AM – 11:30 AM ADI Orthogonal Spline Collocation Method on Non-rectangular
Regions (p. 39)
R. I. Fernandes, The Petroleum Institute, UAE
11:30 AM – 12:00 PM Linearized alternating direction method for constrained linear
least-squares problem (p. 38)
Raymond Chan, The Chinese University of Hong Kong, Hong
Kong
12:00 PM – 12:30 PM Stable Computations with Gaussians (p. 40)
Michael McCourt, Cornell University, USA
Room: CBC A106
Mini-symposium 7
Direct and Inverse Scattering for Wave Propagation
Organizers: Jiguang Sun, Delaware State University, USA
11:00 AM – 11:30 AM Statistical methods applied to the inverse problem in electroneurography (p. 61)
Erkki Somersalo, Case Western Reserve University, USA
11:30 AM – 12:00 PM An Efficient and Stable Spectral Method for Electromagnetic
Scattering from a Layered Periodic Structure (p. 62)
Ying He - Purdue University, USA
15
12:00 PM – 12:30 PM
A Schwarz generalized eigen-oscillation spectral element method
(GeSEM) for 2-D high frequency electromagnetic scattering in
dispersive inhomogeneous media (p. 62)
Xia Ji, Chinese Academy of Sciences, China
2:00 PM – 2:50 PM: Two concurrent plenary talks
Rom: CBC A106
Chair: Max Gunzburger, Florida State University, USA
Discontinuous Galerkin Method for Hamilton-Jacobi Equations and Front Propagation with Obstacles (p. 32)
Room: CBC A112
Chair: Mary Wheeler, University of Texas at Austin, USA
Alternating Direction Implicit (ADI) Methods – a Personal Retrospective (p. 31)
3:00 PM 00 4:00 PM: Four concurrent sessions
Room: CBC C116
Mini-symposium 1
Computational Methods for Multiphase Flow in Porous Media
Organizer: Zhangxing Chen, University of Calgary, Canada
3:00 PM – 3:30 PM Simulation of Multiphase Flow in Porous Media using Locally
Conservative Finite Element Methods (p. 43)
Shuyu Sun, KAUST, Kingdom of Saudi Arabia
3:30 PM – 4:00 PM Mathematical Analysis of Problems in Filtration Applications
(p. 43)
E.W. Jenkins, Clemson University, USA
Room: CBC C118
Mini-symposium 5
Numerical Analysis and Computations of Fluid Flow Problems
Organizers: Monika Neda, University of Nevada Las Vegas, USA
Carolina Manica, Universidade Federal do Rio Grande do Sul, Brasil
16
3:00 PM – 3:30 PM
Bayesian source separation in MEG (p. 52)
Daniela Calvetti, Case Western Reserve University, USA
3:30 PM – 4:00 PM Approximate Deconvolution Large Eddy Simulation of a
Barotropic Ocean Circulation Model (p. 52)
Traian Iliescu, Virginia Tech, USA
Room: CBC A112
Chair: Yanping Lin, The Hong Kong Polytechnic University, Hong Kong
3:00 PM – 3:30 PM B-Spline Collocation Software for PDEs with Efficient
Interpolation-Based Spatial Error Estimation (p. 40)
Paul Muir, Saint Mary’s University, Canada
3:30 PM – 4:00 PM Fast Solution of the Method of Fundamental Solutions for Modified Helmholtz Equations (p. 39)
C.S. Chen, University of Southern Mississippi, USA
Room: CBC A106
Chair: Weimin Han, University of Iowa, USA
3:00 PM – 4:00 PM Networked Computing Laboratory (NCLab) (p. 75)
Pavel Solin, University of Nevada – Reno, USA
4:30 PM – 6:00 PM: Four concurrent sessions
Room: CBC C116
Mini-symposium 1
Organizer: Zhangxing Chen, University of Calgary, Canada
4:30 PM – 5:00 PM Recent Developments in Multipoint Flux Mixed Finite Elements
(p. 42)
Guangri Xue (Gary), Shell, USA
5:00 PM – 5:30 PM A numerical method for solving 3D elastic wave equation in
anisotropic heterogeneous medium (p. 42)
Wenyuan Liao, University of Calgary, Canada
17
Room: CBC C118
Mini-symposium 5
4:30 PM – 5:00 PM Modern ideas in turbulence confront legacy codes (p. 53)
William Layton, University of Pittsburgh, USA
5:00 PM – 5:30 PM
5:30 PM – 6:00 PM
Numerical free surface flows on dynamic octree meshes (p. 53)
Maxim Olshanskii, Moscow State University, Russia
The dynamics of two phase complex fluids:
drop
formation/pinch-off (p. 55)
Xiaofeng Yang, University of South Carolina, USA
Room: CBC A112
Chair: B. Bialecki, Colorado School of Mines, US
4:30 PM – 5:00 PM A Legendre-Galerkin method of the Helmholtz Equation for Electromagnetics Cavity Problem (p. 40)
Weiwei Sun, City University of Hong Kong, Hong Kong
5:00 PM – 5:30 PM The method of fundamental solutions for the solution of inverse
problems (p. 39)
Andreas Karageorghis, University of Cyprus, Cyprus
5:30 PM – 6:00 PM Expectations and Limitations of the Compact Splitting Method
for Quenching-combustion Problems (p. 41)
Qin Sheng, Baylor University, USA
Room: CBC A106
Mini-symposium 7
4:30 PM – 5:00 PM An eigenvalue method using multiple frequency data (p. 63)
Jiguang Sun, Delaware State University, USA
5:00 PM – 5:30 PM Sparse reconstruction in diffuse optical tomography (p. 63)
Taufiquar Rahman Khan, Clemson University, USA
6:30 PM – 9:30 PM: Banquet at Richard Tam Alumni Center
18
Program
Room: CBC A112
Chair: Shuyu Sun, KAUST, Kingdom of Saudi Arabia
Discrete Stability, DPG Method and Least Squares (p. 31)
L. Demkowicz, ICES, UT Austin, USA
Room: CBC A106
Chair: Gang Bao, Michigan State University, USA
Optimization-Based Methods for Conservative and Monotone Transport and
Remap (p. 30)
Pavel Bochev, Sandia National Laboratories, USA
9:30 AM – 10:30 AM: Four concurrent sessions
Room: CBC C116
Mini-symposium 3
Developing ice-sheet models for the next generation climate simulation
Organizers: Katherine J. Evans, Oak Ridge National Laboratory, USA
Mauro Perego, Florida State University, USA
9:30 AM – 10:00 AM BISICLES – progress on a higher-order adaptive mesh refinement
ice-sheet model (p. 47)
Daniel Martin, Lawrence Berkeley National Lab, USA
10:00 AM – 10:30 AM A simple approach to modeling multi-physics coupled models,
application to large-scale ice sheet models (p. 47)
Helene Seroussi, Caltech-Jet Propulsion Laboratory, USA and
Ecole Centrale Paris, Chatenay-Malabry, France
19
Room: CBC A106
9:30 AM – 10:00 AM Most Likely Paths of Shortfalls in Long-Term Hedging with
Short-Term Futures
Zhijian Wu, University of Alabama, USA
10:00 AM – 10:30 AM Pricing Options under Jump-diffusion Models
Jari Toivanen, Stanford University, Stanford, USA
Room: CBC A112
Mini-symposium 6
9:30 AM – 10:00 AM Cell conservative flux recovery and a posteriori error estimate of
high order finite volume methods (p. 60)
Ming Wang, University of California at Irvine, USA and Peking
University, China
10:00 AM – 10:30 AM A parallel geometric-algebraic multigrid solver for the Stokes
problem (p. 60)
Chensong Zhang, Chinese Academy of Sciences, China
Room: CBC C118
Chair: Huoyuan Duan, Nankai University, China
9:30 AM – 10:00 AM Optimization Under Uncertainty: Models and Computational
Techniques
Ralph Baker Kearfott, University of Louisiana at Lafayette,
USA
10:00 AM – 10:30 AM HDG methods for Reissner-Mindlin plates
Fatih Celiker, Wayne State University, USA
11:00 AM – 12:30 PM: Four concurrent sessions
Room: CBC C116
Mini-symposium 3
20
11:00 AM – 11:30 AM
11:30 AM – 12:00 PM
12:00 PM – 12:30 PM
A method for simulating dynamic ice shelves in global ocean models (p. 48)
Xylar Asay-Davis, Los Alamos National Laboratory, USA
Which physics for coupled ice sheet and ocean models? Lessons
learned from Petermann Glacier (p. 48)
Carl Gladish, New York University, USA
A geometrical multigrid method for shallow ice models based on
an energy minimization approach (p. 49)
Guillaume Jouvet, Free University of Berlin, Germany
Room: CBC A106
Mini-symposium 2
11:00 AM – 11:30 AM Multiple Time Scales and Time Stepping for Ocean Circulation
Models (p. 44)
Robert L. Higdon, Oregon State University, USA
11:30 AM – 12:00 PM Non-Oscillatory Central Finite-Volume Schemes for Atmospheric
Numerical Modeling (p. 45)
Ram Nair, National Center for Atmospheric Research, USA
12:00 PM – 12:30 PM Earth core thermal convection simulation using high-order finite
element (p. 44)
Wei Leng, Chinese Academy of Sciences, China
Room: CBC A112
Mini-symposium 6
11:00 AM – 11:30 AM A BPX preconditioner for the symmetric discontinuous Galerkin
methods on graded meshes (p. 61)
Liuqiang Zhong, South China Normal University, China and
The Chinese University of Hong Kong, Hong Kong
11:30 AM – 12:00 PM On a Robin-Robin domain decomposition method with optimal
convergence rate (p. 61)
Shangyou Zhang, University of Delaware, USA
12:00 PM – 12:30 PM Adaptive finite element techniques for Einstein constraints (p. 61)
Yunrong Zhu, University of California at San Diego, USA
21
Room: CBC C118
Chair: Qi Wang, University of South Carolina, USA
11:00 AM – 11:30 AM A Multiple-Endpoints Chebysheve Collocation Method For High
Order Problems (p. 73)
Zhiping Li, Peking University, China
11:30 AM – 12:00 PM Mortar multiscale methods for Stokes-Darcy flows in irregular
domains (p. 77)
Ivan Yotov, University of Pittsburgh, USA
12:00 PM – 12:30 PM L2 Projected C 0 Elements for non H 1 Very Weak Solution of curl
and div Operators (p. 70)
Huoyuan Duan, Nankai University, China
2:00 PM – 2:50 PM: Two concurrent plenary talks
Room: CBC A106
Chair: Aaron Luttman, National Security Technologies, LLC, USA
Future Directions for Inverse Scattering Problems (p. 29)
Gang Bao, Zhejiang University, China and Michigan State University, USA
Room: CBC A112
Chair: Long Chen, University of California, USA
Multiscale Mixed Methods for Heterogeneous Elliptic Problems (p. 29)
Todd Arbogast, UT Austin, USA
Room: CBC C116
Mini-symposium 3
3:00 PM – 3:30 PM Advanced ice sheet modeling: scalable parallel adaptive full
Stokes solver and inversion for basal slipperiness and rheological parameters (p. 49)
Tobin Isaac, The University of Texas at Austin, USA
22
3:30 PM – 4:00 PM
Scalable and composable implicit solvers for polythermal ice flow
with steep topography (p. 50)
Jed Brown, Argonne National Laboratory, USA
Room: CBC A106
Mini-symposium 5
3:00 PM – 3:30 PM Dual-mixed finite element methods for the Navier-Stokes equations
Jason Howell, Clarkson University, USA
3:30 PM – 4:00 PM An efficient and accurate numerical method for high-dimensional
stochastic partial differential equations
Alexander Labovsky, Michigan Technological University, USA
Room: CBC A112
Mini-symposium 6
3:00 PM – 3:30 PM Algebraic Multigrid Methods for Petroleum Reservoir Simulation
Xiaozhe Hu, The Pennsylvania State University, USA
3:30 PM – 4:00 PM The adaptive nonconforming finite element method for the fourth
order problem
Room: CBC C118
Chair: Pavel Solin, University of Nevada Reno, USA
3:00 PM – 3:30 PM Asymptotic Formulas for the Generalized Stirling Numbers of the
Second Kind with Integer Parameters (p. 81)
Cristina B. Corcino, De La Salle University, Philippines
3:30 PM – 4:00 PM Effects of Rotation on Energy Stabilization of Internal Gravity
Waves Confined in a Cylindrical Basin (p. 83)
Michael Dameron, University of Texas at Brownsville, USA.
23
Room: CBC C116
Chair: Todd Arbogast, University of Texas at Austin, USA
4:30 PM – 5:00 PM Second Order Virtual Node Algorithms for Stokes Flow Problems
with Interfacial Forces and Irregular Domains (p. 79)
Diego C. Assêncio, University of California, Los Angeles, USA
5:00 PM – 5:30 PM
Unconditionally Positive Residual Distribution Schemes for Hyperbolic Conservation Laws (p. 79)
M.E.Hubbard, University of Leeds, UK
5:30 PM – 6:00 PM Immerse Finite Element Methods for Solving Parabolic Type
Moving Interface Problems (p. 85)
Xu Zhang, Virginia Tech, USA
Room: CBC A106
Mini-symposium 5
4:30 PM – 5:00 PM Numerical and analytical study for viscoelastic flow in a moving
domain (p. 54)
Hyesuk Lee, Clemson University, USA
5:00 PM – 5:30 PM Stability and Convergence Analysis: Leray-Iterated-Tikhonov
NSE with Time Relaxation (p. 54)
Carolina Manica, Universidade Federal do Rio Grande do Sul,
Brasil
5:30 PM – 6:00 PM Sensitivity Analysis and Computations for Regularized NavierStokes Equations (p. 55)
Monika Neda, University of Nevada Las Vegas, USA
Room: CBC A112
Mini-symposium 6
4:30 PM – 5:00 PM Multigrid Methods for Stokes Equation based on Distributive
Gauss-Seidel Relaxation (p. 56)
Long Chen, University of California at Irvine, USA
5:00 PM – 5:30 PM Operator splitting methods for stiff convection-reaction-diffusion
equations (p. 58)
Xinfeng Liu, University of South Carolina, USA
5:30 PM – 6:00 PM Covolume-Upwind Finite Volume Approximations for Linear Elliptic Partial Differential Equations (p. 58)
Lili Ju, University of South Carolina, USA
24
Room: CBC C118
Chair: R. Baker Kearfott, Uiversity of Louisiana at Lafayette, USA
4:30 PM – 5:00 PM Discontinuous-in-Space Explicit Runge-Kutta Residual Distribution Schemes for Hyperbolic Conservation Laws (p. 82)
A. Warzyński, University of Leeds, UK
5:00 PM – 5:30 PM
5:30 PM – 6:00 PM
Dispersion and Dissipation Analysis of Two Fully Discrete Discontinuous Galerkin Methods (p. 84)
He Yang, Rensselaer Polytechnic Institute, USA
On Generalized Bell Numbers for Complex Argument (p. 81)
Roberto B. Corcino, De La Salle University, Philippines
25
Program
Room: CBC A106
Chair: Yanping Lin, The Hong Kong Polytechnic University, Hong Kong
Some Algorithmic Aspects of hp-Adaptive Finite Elements (p. 29)
Randolph E. Bank, University of California at San Diego, USA
Room: CBC A112
Chair: Yau Shu Wong, University of Alberta, Canada
Finite element analysis of electromaganetics in metamaterials (p. 32)
Jichun Li, University of Nevada, Las Vegas, USA
9:30 – 10:30: Three concurrent sessions
Room: CBC C116
Chair: Shuhua Zhang, Tianjin University of Economy and Finance, China
9:300 AM – 10:00 AM A balanced finite element method for singularly perturbed
reaction-diffusion problems (p. 76)
M. Stynes, National University of Ireland, Ireland
10:00 AM – 10:30 AM A Potential-based Finite Element Scheme with CGM for Eddy
Current Problems (p. 82)
Tong Kang, Communication University of China, China
Room: CBC A106
Mini-symposium 5
26
9:300 AM – 10:00 AM
10:00 AM – 10:30 AM
On the Leray regularization with fine mesh filtering (p. 53)
Abigail Bowers, Clemson University, USA
Linear solvers for incompressible flow simulations using ScottVogelius elements (p. 55)
Leo Rebholz, Clemson University, USA
Room: CBC A112
Mini-symposium 6
9:300 AM – 10:00 AM An Algebraic Multilevel Preconditioner for Graph Laplacians
based on Matching of Graphs (p. 56)
James Brannick, The Pennsylvania State University, USA
10:00 AM – 10:30 AM Toward a robust hp-adaptive method for elliptic eigenvalue problems (p. 59)
Jeffrey S. Ovall, University of Kentucky, USA
11:00 AM – 12:30 PM: Three concurrent sessions
Room: CBC C116
Chair: Martin Stynes, National University of Ireland, Cork, Ireland
11:00 AM – 11:30 AM Spectral Collocation Methods for Volterra Integro-Differential
Equations (p. 69)
Yanping Chen, South China Normal University, China
11:30 AM – 12:00 PM A High-Order Transport Scheme for Unstructured Atmosphere
and Ocean Climate Models (p. 74)
Todd Ringler, Los Alamos National Laboratory, USA
12:00 PM – 12:30 PM A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics(p. 75)
Dominik Schoetzau, University of British Columbia, Canada
Room: CBC A106
Mini-symposium 5
27
11:00 AM – 11:30 AM
11:30 AM – 12:00 PM
Analysis of stability and errors of IMEX methods for MHD equations (p. 55)
Hoang Tran, University of Pittsburgh, USA
Physics based filtering for the incompressible Leray-α Magnetohydrodynamics equations (p. 55)
Nicholas Wilson, Clemson University, USA
Room: CBC A112
Mini-symposium 6
11:00 AM – 11:30 AM New multigrid methods for the Stokes and linear elasticity problems (p. 58)
Hengguang Li, Wayne State University, USA
11:30 AM – 12:00 PM A treecode elastostatics computation (p. 58)
Hualong Feng, Illinois Institute of Technology, USA
12:00 PM – 12:30 PM Axially symmetric volume constrained anistropic mean curvature
flow (p. 61)
Wenxiang Zhu, Iowa State University, USA
28
Abstracts
Plenary Talks
Multiscale Mixed Methods for Heterogeneous Elliptic Problems
Todd Arbogast, UT Austin, USA
Abstract. We consider a second order elliptic problem with a heterogeneous coefficient written in mixed form. Multiscale approximation methods for these problems can be viewed in
one of three equivalent frameworks: as a Galerkin or finite element method with nonpolynomial basis functions, as a variational multiscale method with standard finite elements, or as
a domain decomposition method with restricted degrees of freedom on the interfaces. Each
is valuable for devising effective local multiscale methods. Taking a nonoverlapping domain
decomposition view, we define a new multiscale mortar space that incorporates information
from homogenization theory to better approximate the solution along the interfaces with
just a few degrees of freedom. In the case of a locally periodic heterogeneous coefficient of
period , the new method achieves both optimal order error estimates in the discretization
parameters and convergence when is small, with no numerical resonance, despite the fact
that our method is purely locally defined. Moreover, we present numerical examples to assess
its performance when the coefficient is not obviously locally periodic. We show that the new
mortar method works well, and better than polynomial mortar spaces.
Some Algorithmic Aspects of hp-Adaptive Finite Elements
Randolph E. Bank, University of California at San Diego, USA
Abstract. We will discuss our on-going investigation of hp-adaptive finite elements. We
will focus on a posteriori error estimates based on superconvergent derivative recovery. Besides providing both global error estimates and local error indicators, this family of error
estimates also provides information that forms the basis of our hp-adaptive refinement and
coarsening strategies. In particular, these a posteriori error estimates address in a cost efficient and natural way the critical issue of deciding between h or p refinement/coarsening.
Some numerical examples will be provided.
Joint with Hieu Nguyen, University of California at Davis, USA.
Future Directions for Inverse Scattering Problems
Gang Bao, Zhejiang University, China and Michigan State University, USA
Abstract. A survey on the recent progress of our research group on three classes of inverse
scattering problems in wave propagation, namely inverse medium scattering, inverse source
scattering, and inverse obstacle scattering, will be presented. Issues on numerical solution,
mathematical analysis, as well as applications will be discussed. Future directions on the
inverse scattering problems and significant new applications will be highlighted.
29
Plenary Talks
Optimization-Based Methods for Conservative and Monotone Transport and
Remap
Abstract. We describe a new optimization-based modeling (OBM) strategy for compatible
discretizations and demonstrate its effectiveness by constructing monotone optimizationbased transport (OBT) and remap (OBR) schemes without limiters.
OBM is a “divide-and-conquer” approach which separates preservation of properties such
as discrete maximum principle, local bounds, or monotonicity from the discretization process. In so doing, our approach obviates severe constraints on mesh geometry and field
representations, thereby greatly improving flexibility of resulting schemes.
In particular, optimization-based transport and remap (OBT/OBR) is formulated as the
solution of a global convex optimization problem in which accuracy considerations, handled
by an objective functional, are separated from monotonicity considerations, handled by a
carefully defined set of inequality constraints.
The resulting methods are provably linearity preserving on grids with arbitrary cell shapes
under more permissive conditions on the mesh motion than a standard explicit transport/remap scheme with, e.g., Van Leer limiting. We demonstrate the scheme on a series
of standard test problems on non-uniform, unstructured grids. This is joint work with D.
Ridzal, K. Peterson, and J. Young.
Challenges in Numerical Simulation of Unconventional Oil and Gas Reservoirs
Zhangxing Chen, University of Calgary, Canada
Abstract. Mathematical models have widely been used to predict, understand, and optimize
complex physical processes in modeling and simulation of multiphase fluid flow in petroleum
reservoirs. These models are important for understanding the fate and transport of chemical
species and heat. With this understanding the models are then applied to the needs of the
petroleum industry to design enhanced oil and gas recovery strategies.
While mathematical modeling and computer simulation have been successful in their application to the recovery of conventional oil and gas, there still exist a lot of challenges in their
application to unconventional oil and gas modeling. As conventional oil and gas reserves
dwindle and oil prices rise, the recovery of unconventional oil and gas (such as heavy oil,
oil sands, tight gas, and shale gas) is now the center stage. For example, enhanced heavy
oil recovery technologies are an intensive research area in the oil industry, and have recently
generated a battery of recovery methods, such as cyclic steam stimulation (CSS), steam
assisted gravity drainage (SAGD), vapor extraction (VAPEX), in situ combustion (ISC),
hybrid steam-solvent processes, and other emerging recovery processes. This presentation
will give an overview on challenges encountered in modeling and simulation of these recovery
processes: insufficient physics/chemistry in current models, multi-scale phenomena, phase
behavior, geomechanics, assisted history matching with closed-loop optimization, transport
of solvents, wellbore modeling, and four-phase flow. It will also present some case studies
for the applications of these recovery processes to real heavy oilfields.
30
Plenary Talks
Discrete Stability, DPG Method and Least Squares
L. Demkowicz, ICES, UT Austin, USA
Abstract. Ever since the ground breaking paper of Ivo Babuska [1], everybody from Finite
Element (FE) community has learned the famous phrase: “Discrete stability and approximability imply convergence.” The challenge in establishing convergence comes from the
fact that, except for a relative small class of “safe” coercive (elliptic) problems, continuous
stability DOES NOT imply discrete stability. In other words, the problem of interest may
be well posed at the continuous level but this does not imply that the corresponding FE
discretization will automatically be stable. No wonder then that the FE numerical analysis
community spent the last 40+ years coming up with different ideas how to generate discretely stable schemes coming up with such famous results as Mikhlin’s theory of asymptotic
stability for compact perturbations of coercive problems, Brezzi’s theory for problems with
constraints, concept of stabilized methods starting with SUPG method of Tom Hughes, the
bubble methods, stabilization through least-squares, stabilization through a proper choice of
numerical flux including a huge family of DG methods starting with the method of Cockburn
and Shu, and a more recent use of exact sequences.
In the first part of my presentation I will recall Babuska’s Theorem and review shortly the
milestones in designing various discretely stable methods listed above.
In the second part of my presentation, I will present the Discontinuous Petrov-Galerkin
method developed recently by Jay Gopalakrishnan and myself [2]. The main idea of the
method is to employ (approximate) optimal test functions that are computed on the fly
at the element level using Bubnov-Galerkin method and an enriched space. If the error
in approximating the optimal test functions is negligible, the method AUTOMATICALLY
guarantees the discrete stability, provided the continuous problem is well posed. And this
holds for ANY linear problem. The result is shocking until one realizes that we are working
with a unconventional least squares method. The twist lies in the fact that the residual lives
in a dual space and it is computed using dual norms.
The method turns out to be especially suited for singular perturbation problems where one
strives not only for stability but also for ROBUSTNESS, i.e. a stability UNIFORM with
respect to the perturbation parameter. I will use an important model problem: convectiondominated diffusion to outline a general strategy for constructing a robust DPG method and
report on recent results obtained in collaboration with Norbert Heuer [3].
References
[1] I. Babuska, Error-bounds for Finite Element Method. Numer. Math, 16, 1970/1971.
[2] L. Demkowicz, J. Gopalakrishnan. A Class of Discontinuous Petrov-Galerkin Methods.
Part II: Optimal Test Functions. Numer. Meth. Part. D. E., 27, 70-105, 2011.
[3] L. Demkowicz, N. Heuer, Robust DPG Method for Convection-Dominated Diffusion
Problems. ICES Report 2011-33, submitted to SIAM J. Num. Anal.
Alternating Direction Implicit (ADI) Methods – a Personal Retrospective
Abstract. For more than half a century, alternating direction implicit (ADI) methods have
proved to be effective techniques for the solution of various multidimensional time–dependent
31
Plenary Talks
problems. Their attraction lies in the fact that they reduce such a problem to the solution
of systems of independent one–dimensional problems. First formulated for finite difference
methods, ADI methods were subsequently extended to various other spatial discretizations
including finite element Galerkin methods, spectral methods and orthogonal spline collocation methods. In this talk, some milestones in their development will be discussed as well
some of their recent applications.
Efficient Numerical Approaches for the Simulation and Control of PDEs with
Random Inputs
Abstract. We discuss three problems involving the numerical solution of PDEs with random
inputs. First, we consider an approach for PDEs driven by white noise in which the problem
is transformed into one driven by correlated noise which can then be efficiently treated using,
e.g., Karhunen-Loeve expansions and sparse grid methods. We then discuss the replacement
of white noise forcing with the perhaps more physically relevant pink noise of, more generally,
1/f α noise. We also discussed methods for discretizing these noises. Finally, we discuss
methods for treating control and optimization problems constrained by PDEs with random
inputs. Collaborators in this work include John Burkardt, Steven Hou, Ju Ming, Miroslav
Stoyanov, Catalin Trenchea, and Clayton Webster.
Reduced Models You can Believe in
Jan S Hesthaven, Brown University, USA
Abstract. In this talk we present an overview of recent and ongoing efforts to develop
reduced basis methods for which one can develop a rigorous a posteriori theory, hence certifying the accuracy of the reduced model for parametrized linear PDEs. This is in contrast
to most previous attempts to develop reduced complexity methods that, while used widely
and of undisputed value, are often heuristic in nature and the validity and accuracy of the
output is often unknown. This limits the predictive value of such models.
We shall outline the theoretical and computational developments of certified reduced basis
methods, drawing from problems in electromagnetics and acoustics, given both on differential
and integral form. The performance of the certified reduced basis model will be illustrated
through a number of examples to highlight the significant advantages of the proposed approach and we discuss extensions and challenges associated with high-dimensional problems
to the extend time permits.
Finite element analysis of electromaganetics in metamaterials
Jichun Li, University of Nevada, Las Vegas, USA
Abstract. In this talk we will report some recent advances in finite element analysis and
simulation of electromaganetics wave propagation in metamaterials. The stability properties, optimal error estimates and superconvergence are considered for various fully discrete
schemes. Numerical tests are presented not only for theoretical justification, but also for
some interesting metamaterial phenomena such as invisibility cloak, and backward wave
propagation etc.
This talk is based on the joint work with Yunqing Huang and Wei Yang.
32
Plenary Talks
Discontinuous Galerkin Method for Hamilton-Jacobi Equations and Front Propagation with Obstacles
Abstract. In this talk we will first describe a discontinuous Galerkin (DG) method for solving Hamilton-Jacobi equations, including those for front propagation problems. This method
solves the Hamilton-Jacobi equations directly, without first converting them to conservation
law systems, can be proved to converge optimally in L2 for smooth solutions, and perform
nicely for viscosity solutions with singularities. We then extend the DG method to front
propagation problems in the presence of obstacles. We follow the formulation of Bokanowski
et al. leading to a level set formulation driven by min(ut + H(x, ∇u), u − g(x)) = 0, where
g(x) is an obstacle function. The DG scheme is motivated by the variational formulation
when the Hamiltonian H is a linear function of ∇u, corresponding to linear convection
problems in presence of obstacles. The scheme is then generalized to nonlinear equations,
resulting in an explicit form which is very efficient in implementation. Stability analysis are
performed for the linear case with Euler forward, a second and third order SSP Runge-Kutta
time discretization, and convergence is proved for the linear case with Lipschitz continuous
and piecewise smooth data. Numerical examples are provided to demonstrate the robustness of the method. Finally, a narrow band approach is considered in order to reduce the
computational cost. This is a joint work with Yingda Cheng (the design of the scheme), Tao
Xiong (error estimates for smooth solutions), and Olivier Bokanowski and Yingda Cheng
(front propagation without and with obstacles).
Coupling Compositional Flow, Transport, and Mechanics in Porous Media for
Modeling Carbon Sequestration in Saline Aquifers
Mary F. Wheeler, The University of Texas at Austin, USA
Abstract. A key goal of our work is to produce a prototypical computational system to
accurately predict the fate of injected CO2 in conditions governed by multiphase flow, rock
mechanics, multi-component transport, thermodynamic phase behavior, chemical reactions
within both the fluid and the rock, and the coupling of all these phenomena over multiple
time and spatial scales. Even small leakage rates over long periods of time can unravel the
positive effects of sequestration. This effort requires high accuracy in the physical models
and their corresponding numerical approximations. For example, an error of one percent per
year in a simulation may be of little concern when dealing with CO2 oil recovery flooding,
but such an inaccuracy for sequestration will lead to significantly misleading results that
could fail to produce any long-term predictive capability. It is important to note that very
few parallel commercial and/or research software tools exist for simulating complex processes
such as coupled multiphase flow with chemical transport and geomechanics.
Here we discuss modeling multicomponent, multiscale, multiphase flow and transport through
porous media and through wells and that incorporate uncertainty and history matching and
include robust solvers. The coupled algorithms must be able to treat different physical
processes occurring simultaneously in different parts of the domain, and for computational
accuracy and efficiency, should also accomodate multiple numerical schemes. We present a
new multipint flux mixed finite element method for compositional flow as well as discuss
some carbon seqestration results in saline aquifers.
33
Plenary Talks
Optimal Discretization, Adaptation and Iterative Solver for High Order Partial
Differential Equations
Jinchao Xu, Penn State University, USA
Abstract. In this talk, I should discuss about an universal construction of finite element
discretization methods for high order PDEs in any dimensions (joint work with M. Wang),
optimal grid adaptation (joint work with J. Hu) and optimal algebraic solvers (joint work
with S. Zhang) for these finite elements.
Unclaimed Territories of Superconvergence I: Spectral and Spectral Collocation
Methods
Abstract. In numerical computation, we often observe that the convergent rate exceeds
the best possible global rate at some special points. Those points are called superconvergent
points, and the phenomenon is called superconvergence phenomenon, which is well understood for the h-version finite element method. However, the relevant study for the p-version
finite element method and the spectral method is lacking.
In this work, superconvergence properties for some high-order orthogonal polynomial interpolations are studied. The results are twofold: When interpolating function values, we
identify those points where the first and second derivatives of the interpolant converge faster;
When interpolating the first derivative, we locate those points where the function value of
the interpolant superconverges. For both cases we consider various Chebyshev polynomials,
but for the latter case, we also include the counterpart Legendre polynomials.
34
A Special Session in Honor of Walter Allegretto’s 70th
Birthday
Organizers: Yau Shu Wong, University of Alberta, CA
Hongtao Yang, University of Nevada, Las Vegas, USA
A Molecular Dynamics-Continuum Coupled Model for Heat Transfer in Composite Materials
Jizu Huang, Chinese Academy of Sciences, China
Liqun Cao∗ , Chinese Academy of Sciences, China
Sam Yang, Clayton South MDC, Australia
Abstract. In this talk, we discuss the heat transfer problem in composite materials which
contain the nano-scale interface. A molecular dynamics-continuum coupled model is developed to study the heat transport from the macroscale to the microscale. The model includes
four major steps: (1) A reverse non-equilibrium molecular dynamics (RNEMD) is used to
calculate some physical parameters such as the thermal conductivities on the interface. (2)
The homogenization method is applied to compute the homogenized thermal conductivities
of composite materials. (3) We employ the multiscale asymptotic method for the macroscopic heat transfer equation to compute the temperature field in the global structure of
composite materials. (4) We develop a molecular dynamics-continuum coupled model to
reevaluate the temperature field of composite materials, in particular, the local temperature
field near the interface. The numerical results in one-, two- and three-dimensional structures
of composite materials including the nano-scale interface are given. Good agreement between
the numerical results of the proposed coupled algorithm and those of the full MD simulation
is found, demonstrating the accuracy of the present method and its potential applications
in the thermal engineering of composite materials.
A Variational Approach for Exact Histogram Specification
Raymond Chan∗ , Mila Nikolova, and You-Wei Wen, The Chinese University of Hong Kong,
Hong Kong
Abstract. We focus on exact histogram specification when the input image is quantified.
The goal is to transform this input image into an output image whose histogram is exactly
the same as a prescribed one. In order to match the prescribed histogram, pixels with the
same intensity level in the input image will have to be assigned to different intensity levels in
the output image. An approach to classify pixels with the same intensity value is to construct
a strict ordering on all pixel values by using auxiliary attributes. Local average intensities
and wavelet coefficients have been used by the past as the second attribute. However,
these methods cannot enable strict-ordering without degrading the image. In this paper, we
propose a variational approach to establish an image preserving strict-ordering of the pixel
values. We show that strict-ordering is achieved with probability one. Our method is image
preserving in the sense that it reduces the quantization noise in the input quantified image.
Numerical results show that our method gives better quality images than the preexisting
methods.
35
A Direction Splitting Algorithm for Flow Problems in Complex/Moving Geometries
Peter Minev, University of Alberta, Edmonton, Canada
Abstract. An extension of the direction splitting method for the incompressible NavierStokes equations proposed in [1], to flow problems in complex, possibly time dependent
geometries will be presented. The idea stems from the idea of the fictitious domain/penalty
methods for flows in complex geometry. In our case, the velocity boundary conditions on
the domain boundary are approximated with a second-order of accuracy while the pressure
subproblem is harmonically extended in a fictitious domain such that the overall domain
of the problem is of a simple rectangular/parallelepiped shape. The new technique is still
unconditionally stable for the Stokes problem and retains the same convergence rate in both,
time and space, as the Crank-Nicolson scheme. A key advantage of this approach is that
the algorithm has a very impressive parallel performance since it requires the solution of
one-dimensional problems only, which can be performed very efficiently in parallel by a
domain-decomposition Schur complement approach. Numerical results illustrating the convergence of the scheme in space and time will be presented. Finally, the implementation of
the scheme for particulate flows will be discussed and some validation results for such flows
will be presented.
[1] J.L. Guermond, P.D. Minev, A new class of massively parallel direction splitting for
the incompressible Navier-Stokes equations. Computer Methods in Applied Mechanics and
Engineering, 200 (2011), 2083–2093.
Homogenization and parameter estimation of reaction-diffusion systems with
rough boundaries
Chiara Mocenni, University of Siena, Italy
Abstract. The talk addresses the problem of parametrizing the boundary data for reactiondiffusion partial differential equations associated to distributed systems that possess rough
boundaries. The boundaries are modeled as fast oscillating periodic structures and are
endowed with Neumann or Dirichlet boundary conditions. Using techniques from homogenization theory and multiscale analysis we derive the effective equations and boundary
conditions that are satisfied by the homogenized solution. Numerical simulations that validate the theoretical results are presented and compared with the alternative approach based
on solving the same equation with a smoothed version of the boundary. We numerically
explore the dynamics of the homogenized solutions and show dynamical regime shifts that
include the anticipation of pattern formation as a result of the variation of the diffusion
coefficient. The problem of estimating the diffusion parameter of the homogenized system is
finally addressed by means of a nonlinear identification procedure and a linear least square
approach applied to finite element discretized equations.
Joint work with Emiliano Sparacino (Department of Information Engineering, University of
Siena, Italy) and Jorge Passamani Zubelli (IMPA, Rio de Janeiro, Brasil)
Periodic solutions to nonlinear equations with oblique boundary conditions
Walter Allegretto, University of Alberta, Canada
Duccio Papini∗ , Università degli Studi di Siena, Italy
Abstract. We study the existence of positive periodic solutions to nonlinear elliptic and
36
parabolic equations with oblique and dynamical boundary conditions and non-local terms.
We observe that the oblique boundary conditions problems we consider would arise in situations where the motion due to diffusion induced an effect in a different direction, for
example in the situation of charged bacteria moving in a magnetic field. On the other hand,
the dynamic boundary condition could be used to model situations where the biological
species was stored and released depending on conditions at the boundary. The results are
obtained through fixed point theory, topological degree methods and properties of related
linear elliptic problems with natural boundary conditions and possibly non-symmetric principal part. As immediate consequences, we also obtain estimates on the principal eigenvalue
for non-symmetric elliptic eigenvalue problems.
A Front-fixing Finite Element Method for the Valuation of American Options
with Regime Switching
A. D. Holmes, Deloitte & Touche LLP, Houston, USA
Hongtao Yang, University of Nevada, Las Vegas, USA
Shuhua Zhang∗ , Tianjin University of Finance and Economics, China
Abstract. American option problems under regime switching model are considered in this
paper. The conjectures about the position of early exercise prices are proved, which generalize the results in the previous literature by allowing the interest rates are different in two
states. A front-fixing finite element method for the free boundary problems are proposed and
implemented. Its stability is established under reasonable assumptions. Numerical results
are given to examine the rate of convergence of our method and compare it with the usual
finite element method.
Mixed finite element analysis of thermally coupled non-Newtonian flows
Jiansong Zhang, China University of Petroleum, China
Jiang Zhu∗ , Laboratório Nacional de Computação Cientı́fica, Brazil
Xijun Yu, Chinese Academy of Sciences, China
F. D. Loula, Laboratório Nacional de Computação Cientı́fica, Brazil
Abstract. In this paper, we consider an incompressible non-Newtonian flow with a temperature dependent viscosity obeying a power law, and the thermal balance includes viscous
heating. The corresponding mathematical model can be written as:

−2∇· (µ(θ)|D(u)|r−2 D(u)) + ∇p = f
in Ω




∇· u = 0
in Ω

r
−∆θ = µ(θ)|D(u)| in Ω


u =0
on Γ



θ =0
on Γ
where u : Ω → IRd is the velocity, p : Ω → IR is the pressure, θ : Ω → IR is the temperature,
Ω is a bounded open subset of IRd , d = 2 or 3, Γ its boundary. The viscosity µ is a function
of θ, µ = µ(θ). D(u) = 21 (∇u + ∇uT ) is the strain rate tensor, and 1 < r < ∞.
We first establish existence and uniqueness of the weak solution of the system of equations.
Next, we propose mixed finite element approximation combined with a fixed point algorithm.
Finally we present convergence analysis with an error estimate between continuous solution
and its iterative finite element approximation.
37
A Special Session in Honor of Graeme Fairweather’s
70th Birthday
Organizers: Yanping Lin, The Hong Kong Polytechnic University, Hong Kong
Orthogonal Spline Collocation for Quasilinear Parabolic Problems with Nonlocal
Boundary Conditions
B. Bialecki∗ , Colorado School of Mines, USA
G. Fairweather, American Mathematical Society, USA
J. C. López-Marcos, Universidad de Valladolid, Spain
Abstract. We formulate and analyze the extrapolated Crank-Nicolson orthogonal spline
collocation method for the solution of quasilinear parabolic problems in one space variable
with nonlocal boundary conditions involving integrals of the unknown solution over the
spatial interval. Using an extension of the analysis of Douglas and Dupont for Dirichlet
boundary conditions, we derive optimal order error estimates in the discrete maximum norm
in time and the continuous maximum norm in space. We discuss the solution of the linear
system arising at each time level via the capacitance matrix technique and the package
COLROW for solving almost block diagonal linear systems. We present numerical examples
that confirm the theoretical error estimates.
A Space-time Domain Decomposition Method for Stochastic Parabolic Problems
Xiao-Chuan Cai, University of Colorado at Boulder, USA
Abstract. We discuss an implicit space-time approach for solving stochastic parabolic
PDEs. We first decouple the space-time discretized stochastic equation into some uncoupled
deterministic systems by using a Karhunen-Loeve expansion and double orthogonal polynomials. And then a multilevel overlapping domain decomposition method is combined with a
recycling GMRES method to solve the large number of systems with similar structures. We
report experiments obtained on a parallel computer with a large number of processors. This
is a joint work with Cui Cong.
Linearized alternating direction method for constrained linear least-squares problem
Raymond H. Chan∗ , The Chinese University of Hong Kong, Shatin, NT, Hong Kong,
China
Min Tao, Nanjing University of Posts and Telecommunications, China
Xiaoming Yuan, Hong Kong Baptist University, Hong Kong, China
Abstract. We apply the alternating direction method (ADM) to solve a constrained linear
least-squares problem where the objective function is a sum of two least-squares terms and
the constraints are box constraints. Using ADM, we decompose the original problem into
two easier least-squares subproblems at each iteration. To speed up the inner iteration, we
linearize the subproblems whenever their closed-form solutions do not exist. We prove the
convergence of the resulting algorithm and apply it to solve some image deblurring problems.
We show the efficiency of our algorithm by comparing it with Newton-type methods.
38
The research is supported in part by HKRGC Grant No. CUHK400510 and CUHK Direct
Allocation Grant 2060408, the Scientific Research Foundation of Nanjing University of Posts
and Telecommunications (NY210049), and a General Research Fund grant of Hong Kong
Fast Solution of the Method of Fundamental Solutions for Modified Helmholtz
Equations
C.S. Chen, University of Southern Mississippi, USA
X.R. Jiang and Wen Chen, Hohai University, China
Abstract. Since 1990s, the method of fundamental solutions (MFS) has re-emerged as an effective meshless method. Instead of boundary discretization as classical BEM, the boundary
collocation points were used in the solution process of the MFS. In the MFS, the singularity
is avoided by the use of fictitious boundary outside the domain. One of the reasons that the
MFS is getting popular is due to its simplicity. By coupling the method of particular solutions (MPS), the MFS has been successfully extended to solving inhomogeneous problems.
In the MFS-MPS approach, two dense matrix systems need to be solved. The development
of the compactly supported radial basis functions (CS-RBFs) has made it possible for formulate the sparse matrix in the context of the MFS. It is desirable that MFS-MPS has the
combined features of ‘sparse’ and ‘meshless’. It is the purpose of this presentation to show
how the sparse formulation of the MFS for the modified Helmholtz equation can be achieved.
ADI Orthogonal Spline Collocation Method on Non-rectangular Regions
R. I. Fernandes∗ , The Petroleum Institute, UAE
B. Bialecki, Colorado School of Mines, USA
Abstract. The alternating direction implicit (ADI) method is a highly efficient technique
for solving multi-dimensional problems on rectangles. When the ADI technique is coupled
with orthogonal spline collocation (OSC) we not only obtain the global solution efficiently
but also observe superconvergence phenomena, that is, at certain points of the domain the
derivative values converge to that of the exact solution at a rate higher than one would
expect from the spline approximation.
In a recent paper (SISC, v. 28 (2006), pp. 1054-1077), we used a Crank Nicolson ADI OSC
method for solving general nonlinear parabolic problems with Robin’s boundary conditions
on rectanglular polygons and demonstrated numerically the accuracy and superconvergence
phenomena in various norms. A natural question that arises is: Does this technique have a
natural extension to non-rectangular regions? In this talk, we present a simple idea of how
the ADI OSC technique can be extended to some such regions. Our approach depends on
the fourth order transfer of Dirichlet boundary conditions in the solution for a two-point
boundary value problem using a non-uniform grid. We illustrate our idea for the solution of
the heat equation on the unit disc.
The method of fundamental solutions for the solution of inverse problems
Abstract. The method of fundamental solutions (MFS) is a relatively new technique
which can be used for the numerical solution of certain boundary value problems and initial/boundary value problems. The ease with which it can be implemented and its effectiveness have made it very popular for the solution of a large variety of problems arising
39
in science and engineering. Recently, it has been used extensively for a particular class of
such problems, namely inverse problems. We attempt to review the applications of the MFS
to the various classes of inverse and related problems, over the last few years. Some of the
several issues related to the implementation of the MFS to such problems are discussed and
some representative numerical results are presented.
Stable Computations with Gaussians
Michael McCourt, Cornell University, USA
Abstract. Radial basis functions (RBFs), or kernels, are used in machine learning, geostatistics, computer graphics, boundary value problems and many other applications. Their
practical application is often impeded by ill-conditioning present for certain choices of RBF.
The most common choice, the Gaussian, is optimal for approximating sufficiently smooth
functions, but also the most susceptible to conditioning issues and thus the least trustworthy
in many circumstances. This work provides a new way to compute and evaluate Gaussian
RBF interpolants in a stable way in arbitrary dimensions with a focus on increasingly flat
kernels. Motivated by the pioneering research of Bengt Fornberg and his co-workers, an
eigenfunction (or Hilbert-Schmidt) expansion of the Gaussian is used to isolate ill-conditioned
terms analytically. In addition to obtaining the true RBF interpolant, this technique can
also be used to produce a highly accurate least-squares approximation at significantly less
cost. Interpolation and regression results will be presented, as well as collocation results for
boundary value problems.
B-Spline Collocation Software for PDEs with Efficient Interpolation-Based Spatial Error Estimation
Paul Muir, Saint Mary’s University, Canada
Abstract. BACOL, recently developed collocation software for 1D parabolic PDEs, has
been shown to be efficient, reliable and robust, especially for problems with solutions exhibiting sharp layers, and for stringent tolerances. The software features adaptive control of
estimates of the spatial and temporal errors. While the BACOL spatial error estimates are
generally quite reliable, the error estimation algorithm involves the (expensive) computation
of two collocation solutions of orders p and p + 1. (The solution of order p + 1 is used to
provide a spatial error estimate for the solution of order p.) This talk will discuss recent
work investigating more efficient spatial error estimation algorithms based on (i) an order
p + 1 (superconvergent) interpolant that allows us to avoid the computation of the higher
order collocation solution, and (ii) an order p interpolant, whose error agrees asymptotically
with the error of the order p collocation solution, that allows us to avoid the computation
of the lower order collocation solution. We have implemented a new, more efficient version
of BACOL based on these new error estimation schemes that we call BACOLI. We provide
numerical results comparing the original version of BACOL with this new version and show
that BACOLI is about twice as fast as the original code.
This is joint work with Tom Arsenault, University of Western Ontario, Tristan Smith, Bank
of Nova Scotia, Jack Pew, Saint Mary’s University, and Zhi Li, Saint Mary’s University.
A Legendre-Galerkin method of the Helmholtz Equation for Electromagnetics
40
Cavity Problem
Weiwei Sun, City University of Hong Kong, Hong Kong
Abstract. We study the TM (transverse magnetic) case of the electromagnetic scattering
from a two-dimensional large rectangular open cavity embedded in an infinite ground plane.
By introducing a non-local transparent boundary condition on the aperture, the governing
equation for this open cavity problem is then reduced to a Holmholtz equation in the rectangular cavity. A Legendre-Gauss interpolatory approximation is devised for the evaluation of
the hyper-singular integral operator, and a Legendre-Galerkin scheme is proposed for solving
the reduced Helmholtz equation. The existence and the uniqueness of the approximation
solution are established for arbitrary wave numbers. The stability and the spectral convergence of the approximation scheme are then proved. Illustrative numerical results, which are
in agreement with the theoretical estimates, are presented.
Expectations and Limitations of the Compact Splitting Method for Quenchingcombustion Problems
Qin Sheng∗ and Matt Beauregard, Baylor University, USA
Abstract. This talk is based on a collaborated endeavor with a family of compact splitting schemes for solving two-dimensional singular reaction-diffusion equations for combustion
simulations. While a temporal adaption is utilized, uniform grids are enforced in the space.
We will show that the compact splitting scheme is numerically stable and convergent when
its dimensional Courant numbers are within certain frames of windows determined by the
given spatial domain. Though such a window poses a considerable restriction on decomposed
compact computations, the interesting combination of different computational technologies
is in fact highly efficient and reliable for a variety of combustion applications. Some experimental results will be given to illustrate our conclusions and concerns. We will also
show that the compact splitting method studied is sufficiently accurate in determining the
most important key characteristics such as the quenching time, critical domain and blow-up
profiles.
41
Mini-symposia
Mini-symposium 1:
Organizer: Zhangxin Chen, University of Calgary, Canada
Recent Developments in Multipoint Flux Mixed Finite Elements
Guangri Xue (Gary), Shell, USA
Abstract. We report recent developments in multipoint flux mixed finite element (MFMFE)
method on flow in porous media. The MFMFE method gives a cell-centered scheme based
on an appropriate choice of numerical quadrature and degrees of freedom. In addition, the
method is shown to be accurate on highly distorted quadrilaterals and hexahedral grids.
Theoretical results indicate first-order convergence for the pressure and face flux. Numerical
results on single and two-phase flow will be presented. If time allows, the coupling of flow
and elasticity will be also demonstrated.
This is joint work with M. Wheeler and I. Yotov.
A numerical method for solving 3D elastic wave equation in anisotropic heterogeneous medium
Wenyuan Liao, University of Calgary, Canada
Abstract. It is well-known that the acoustic isotropic models of the earth do not adequately
describe the seismic wave propagation in realistic cases, as some important information of
the media is lost when such simplifications were taken. To address these issues, one should
consider elastic wave equation and remove the standard assumption of isotropy of the earth.
Such changes result in better description of the medium properties but meanwhile make
the numerical simulation a computationally challenging task. In this talk a new numerical
method that combines a second-order finite difference approximation in spatial derivatives
and Rosenbrock method for time integration will be introduced to solve the 3D elastic wave
equation in anisotropic medium. We first transform the second-order (in time) elastic wave
equation into a coupled first-order system, which is discretized in space then the semi-discrete
ODE system is solved by high-order Rosenbrock method. We investigate in great details on
the stability, convergence, computational efficiency and numerical dispersion of the new
method. Several numerical examples are conducted to valid the theoretical analysis.
Based on Expert Knowledge and Topological Similarities
Jiang Xie and Wu Zhang∗ , Shanghai University, China
Abstract. Similarities between different biomolecular networks have important significance
in studies of diseases and evolution. Bio-molecular networks are complex networks. Searching
a sub-network which is most similar to a target is a NP-complete problem. It involves
large-scale computations and is time consuming. A new algorithm is developed to search
similar sub-network in one or between two species biomolecular networks. Models of both
mathematics and computation are studied for the searching problem, and the highlights of
the new algorithm are based on expert knowledge and average topological similarities, so as
to improve accuracy of computational results. The range of the free parameter ω is given
42
Mini-symposia
when searching by neighbors-in-first, which can reduce computational complexity. To deal
with large- scale biomolecular networks, the GPU algorithm is also introduced here.
Mathematical Analysis of Problems in Filtration Applications
E.W. Jenkins∗ and V.J. Ervin, Clemson University, USA
Abstract. Filtration applications appear in a variety of physical settings; among them
are industrial filtration for polymer processing, protein separation in pharmaceutical drug
purification, and oil and air filtration in the automotive industry. Effective filters remove
large amounts of debris, but cost considerations warrant filters that have long lifetimes.
Thus, one must balance the need for effective filters against the costs of replacement; filters
that trap everything would have short life spans. Alternatively, one could make a filter last
forever by trapping nothing.
Filter design can be evaluated using computational simulators and optimization tools that
balance these competing objectives. We have used population-based methods, e.g. genetic
algorithms, to evaluate the competing objectives in one-layer filter designs. These methods
thoroughly search the design space to generate a Pareto set of optimal solutions, making
them computationally expensive. Accurate and efficient simulation tools are required to
improve the validity of the solutions generated as well as reduce the computational time
required as we move to more complicated filter designs.
In this talk, we present our work on several mathematical problems that have been motivated by filtration applications. In particular, we discuss results on coupled Stokes/Darcy
systems for generalized, non-Newtonian fluids, and results from optimization studies we have
performed using an existing computational tool for simulation of filtration processes. We
also discuss our current research directions for this class of problems.
Simulation of Multiphase Flow in Porous Media using Locally Conservative Finite Element Methods
Shuyu Sun, KAUST, Kingdom of Saudi Arabia
Abstract. Multiphase flow in porous media has important applications in petroleum reservoir engineering and environmental science. Modeling equation system of such multiphase
flow can be generally split into 1) an elliptic partial differential equation (PDE) for the pressure and 2) one or multiple convection dominated convection-diffusion PDE for the saturation
or for the chemical composition. Accurate simulation of the phenomena not only requires
local mass conservation to be retained in discretization, but it also demands steep gradients
to be preserved with minimal oscillation and numerical diffusion. The heterogeneous permeability of the media often comes with spatially varied capillary pressure functions, both
of which impose additional difficulties to numerical algorithms. To address these issues,
we solve the saturation equation (or species transport equation) by discontinuous Galerkin
(DG) method, a specialized finite element method that utilizes discontinuous spaces to approximate solutions. Among other advantages, DG possesses local mass conservation, small
numerical diffusion, and little oscillation. The pressure equation is solved by either a mixed
finite element (MFE) scheme or a Galerkin finite element method with local conservative
postprocessing. In this talk, we will present the theory and numerical examples of this
combined finite element approach for simulating subsurface multiphase flow.
43
Mini-symposia
Mini-symposium 2:
Abstract. Climate modeling is a multi-facet endeavor. The exponential growth in computational resources encourages ultra high resolution numerical simulations of the global
climate system, which has led to manifestation of unprecedented detail on both global and
local scales. On the other hand, alternatives to ultra high resolution simulations are being
actively pursued. The alternatives include, but not limited to, multi-resolution simulations,
development of scale-invariant subgrid closure schemes, and design of hierarchical conceptual models. One classical research direction that has proven critical for advances in climate
modeling is the discovery of new numerical techniques in spatial discretization and time
stepping schemes. These new techniques may lead to a high-order accuracy, or to certain
desirable conservative properties. On the other front, mathematicians have been studying
the geophysical flows from a dynamical point of view for a long time. Dynamical theory
can qualitatively predict the long time behaviors of the climate system, or the bifurcation
and/or phase transition in the system.
The purpose of this mini-symposium is to bring together researchers working on climate
modeling from a plethora of approaches, and thus to encourage discussions regarding the
advantage and disadvantage of each approach. This conference is primarily on applied and
computational mathematics. Having a mini-symposium on climate modeling within this
conference will help to expose the abundance of problems in climate modeling to the general
community of applied and computational mathematicians.
Multiple Time Scales and Time Stepping for Ocean Circulation Models
Robert L. Higdon, Oregon State University, USA
Abstract. Numerical ocean models admit motions that vary on a wide range of time scales.
For reasons of computational efficiency, it is common practice to split the dynamics into two
subsystems that are solved by different techniques. A vertically-integrated two-dimensional
subsystem can be used to model the fast external waves, and the remaining slow motions
can be modeled with a three-dimensional system that is solved explicitly with a long time
step. A successful implementation of this idea requires a derivation of sufficiently accurate
split equations, combined with proper communication between the two subsystems when
these subsystems are discretized numerically. The latter is partly a matter of the basic
time-stepping schemes that are used, and partly a matter of details of communication. For
example, the algorithms for mass conservation in the two subsystems must yield consistent
results, and the enforcement of this consistency has the effect of filtering the fast motions
from the 3-D mass conservation equations, so that a long time step can be used for the 3-D
equations. This talk will provide a survey of previous and upcoming work on the above
issues.
Earth core thermal convection simulation using high-order finite element
Wei Leng, State Key Laboratory of Scientific and Engineering Computing, Chinese Academy
of Sciences, China
Abstract. Earth core thermal convection simulation is a basic part of the magnetohydrody44
Mini-symposia
namics simulation of the Earth’s magnetic field. In the numerical simulation of core thermal
convection problem, highly accurate numerical results, including the rotation speed, are
obtained using high-order finite element discretization. A special preconditioner which combines the PCD (pressure Convection Diffusion) preconditioner and the geometric multigrid
preconditioner is designed, to circumvent the difficulties in solving the linear systems of equations which contain the anti-symmetric part caused by the Coriolis force term. Numerical
experiments show that our preconditioning strategy is highly efficient.
Non-Oscillatory Central Finite-Volume Schemes for Atmospheric Numerical Modeling
Ram Nair, National Center for Atmospheric Research, USA
Abstract. The central finite-volume (FV) schemes are a subset of Godunov-type methods
for solving hyperbolic conservation laws. Unlike the upwind methods,the central schemes
do not require characteristic decomposition of the hyperbolic system or expensive Riemann
solvers. A semi-discretized central finite-volume scheme has been developed for atmospheric
modeling applications. The non-oscillatory property of the scheme is achieved by employing
high-order weighted essentially non-oscillatory (WENO) reconstruction method, and time integration relies on explicit Runge-Kutta method.The scheme is computationally efficient and
uses a compact computational stencil, amenable to parallel implementation. The central FV
scheme has optional monotonic (positivity-preserving) filter, which is highly desirable for atmospheric tracer transport problems. The scheme has been validated for several benchmark
advection tests on the cubed-sphere. A global shallow-water model and a 2D non-hydrostatic
Euler solver are also developed based on the same central finite-volume scheme, the results
will be presented in the seminar.
On the quasi-hydrostatic ocean models
Antoine Rousseau, INRIA, France
Abstract. In this talk, we want to study the influence of the so-called traditional approximation in the equations of large scale ocean. We will distinguish three main models:
the (traditional) hydrostatic equations (also called primitive equations), the non-hydrostatic
equations, and an intermediate model called quasi-hydrostatic. The quasi-hydrostatic model
consists in adding nontraditional Coriolis terms to the traditional primitive equations. We
will see that we can extend well-posedness results previously established for the primitive
equations, and the corresponding quasi-geostrophic regime will be studied, leading to a new
tilted QG model.
Tropical Cyclogenesis and Vertical Shear in a Moist Boussinesq Model
Leslie Smith∗ and Qiang Deng, University of Wisconsin, Madison, USA
Andrew J. Majda, Courant Institute for Mathematical Sciences, NYU, USA
Abstract. Tropical cyclogenesis is studied in the context of idealized three-dimensional
Boussinesq dynamics with a simple self-consistent model for bulk cloud physics. With lowaltitude input of water vapor, numerical simulations capture the formation of vortical hot
towers. From measurements of water vapor, vertical velocity, vertical vorticity and rain, it is
demonstrated that the structure, strength and lifetime of the hot towers is similar to results
from models including more detailed cloud microphysics. The effects of low-altitude vertical
shear are investigated by varying the initial zonal velocity profile. In the presence of weak
45
Mini-symposia
low-level vertical shear, the hot towers retain the low-altitude monopole cyclonic structure
characteristic of the zero-shear case (starting from zero velocity). Some initial velocity
profiles with small vertical shear can have the effect of increasing cyclonic predominance of
individual hot towers in a statistical sense, as measured by the skewness of vertical vorticity.
Convergence of horizontal winds in the atmospheric boundary layer is mimicked by increasing
the frequency of the moisture forcing in a horizontal sub-domain. When the moisture forcing
is turned off, and again for zero shear or weak low-level shear, merger of cyclonic activity
results in the formation of a larger-scale cyclonic vortex. An effect of the shear is to limit the
vertical extent of the resulting depression vortex. For stronger low-altitude vertical shear, the
individual hot towers have a low-altitude vorticity dipole rather than a cyclonic monopole.
The dipoles are not conducive to the formation of larger-scale depressions, and thus strong
enough low-level shear prevents the vortical-hot-tower route to cyclogenesis. The results
indicate that the simplest condensation and evaporation schemes are useful for exploratory
numerical simulations aimed at better understanding of competing effects such as low-level
moisture and vertical shear.
A Spectral Element Method for the Community Atmosphere Model
Mark Taylor, Sandia National Laboratory, USA
Abstract. We will describe our experience with the spectral element method in the Community Atmosphere Model (CAM). CAM is the the atmospheric component of Community
Earth System Model, one of the flagship U.S. global climate change models. The spectral
element method is a numerically efficient way to obtain a high-order accurate, explicit-intime numerical method. It retains these properties on the unstructured and block structured
grids needed for spherical geometry. Because of its reliance on quadrilateral elements and
tensor-product Gauss-Lobatto quadrature, its fundamental computational kernels look like
dense matrix-vector products which map well to upcoming computer architectures. Here
we will describe our work adapting the spectral element method for atmospheric modeling:
obtaining conservation and non-oscillatory advection. For conservation we have developed
a mimetic/compatible formulation of the method, which allows for exact conservation (machine precision) of quantities solved in conservation form, and semi-discrete conservation
(exact with exact time-discretization) of other quantities such as energy and potential vorticity. For tracer advection in CAM, the spectral element mimetic formulation allows us
to introduce a family of locally bounds preserving limiters. The limiters require solving a
contained optimization problem that is local to each element.
This is a joint work with K.J. Evans, A. Fournier, O. Guba, P. H. Lauritzen and M. Levy.
Mini-symposium 3:
Abstract. The need for accurate, feasible and reliable ice-sheet numerical Simulations at
the continental scale creates significant mathematical and computational challenges. In this
mini-symposium we focus on several aspects of ice sheet numerical simulations ranging from
parallel high performance computing to uncertainty quantification and parameter estimation.
46
Mini-symposia
In particular we will address the design of efficient parallel solvers for large scale simulations
(Greenland and Antarctica ice-sheets); the quantification of uncertainty of numerical solutions and the estimation of model parameters including ice viscosity and bedrock boundary
conditions. Also, we address the problem of coupling ice-sheet model with other climate
sub-models (e.g. ice-ocean coupling).
BISICLES – progress on a higher-order adaptive mesh refinement ice-sheet
model
Daniel Martin, Lawrence Berkeley National Lab, USA
Abstract. Ice sheets require fine resolution to resolve the dynamics of features such as
grounding lines and ice streams. However, ice sheets also have large regions where such high
resolution is unnecessary (much of East Antarctica, for example). Ice sheets are therefore
ideal candidates for adaptive mesh refinement (AMR).
As the Berkeley ISICLES (BISICLES) project, in collaboration with the University of Bristol
in the U.K., we have developed an ice sheet model which uses adaptive mesh refinement in the
horizontal directions to locally refine the computational mesh in regions where fine resolution
is required to accurately resolve ice sheet dynamics. Using coarser meshes in regions where
such fine resolution is unnecessary allows for substantial savings in computational effort.
In addition, the use of the vertically-integrated momentum approximation of Schoof and
Hindmarsh (2010) allows still greater computational efficiency.
We present recent progress and demonstrate the effectiveness of our approach, including
application to regional and continental-scale modeling.
This is a joint work with Stephen Cornford (University of Bristol, UK) and Esmond Ng
(Lawrence Berkeley National Lab, USA).
A simple approach to modeling multi-physics coupled models, application to
large-scale ice sheet models
Helene Seroussi, Caltech-Jet Propulsion Laboratory, USA and Ecole Centrale Paris, ChatenayMalabry, France
Abstract. The recent development of new higher-order, higher-resolution ice sheet models
has shown that sophisticated models are essential to model some areas of the ice sheets,
including the grounding line region. These areas are critical for ice flow projections and
are best simulated using full 3d models. Higher-order models are well suited to ice stream
dynamics, whereas the shallow-shelf approximation is sufficient for modeling ice shelf flow.
Higher-order and full-Stokes model are computationally intensive and prohibitive for largescale modeling. There is therefore a strong need to combine such different models in order
to balance computational cost and physical accuracy for the whole ice sheet.
Here we present a new methodology, the Tiling method, adapted from the Arlequin framework (Ben Dhia, 1998) to couple finite element shelfy-stream, higher-order and Full-Stokes
models. It is achieved by strongly coupling the different approximations within the same
large-scale simulation. This technique is applied to synthetic and real geometries; we compare the results for different hybrid models and single-model approaches.
47
Mini-symposia
This work was performed at the California Institute of Technology’s Jet Propulsion Laboratory and Ecole Centrale Paris under a contract with the National Aeronautics and Space Administration’s Modeling, Analysis and Prediction (MAP) Program (http://issm.jpl.nasa.gov/).
This is a joint work with Mathieu Morlighem (Caltech-Jet Propulsion Laboratory, USA and
Ecole Centrale Paris, France), Eric Larour (Caltech-Jet Propulsion Laboratory, USA), Eric
Rignot (Caltech-Jet Propulsion Laboratory, USA and University of California Irvine, USA)
and Hachmi Ben Dhia (Ecole Centrale Paris, Chatenay-Malabry, France).
A method for simulating dynamic ice shelves in global ocean models
Xylar Asay-Davis, Los Alamos National Laboratory, USA
Abstract. Ice sheets are expected to contribute a major fraction of 21st century sea-level
rise, partly because of nonlinear feedbacks between climate and ice-sheet dynamics. The
rate of ice mass loss is strongly influenced by interactions between the ocean and ice shelves,
huge tongues of floating ice attached to the ice sheet. Theoretical arguments and numerical
simulations indicate that marine ice sheets (those lying on bedrock below sea level) are
subject to an instability that can lead to rapid ice retreat when the bedrock slopes downward
away from the ocean, as is the case in much of West Antarctica. Accurate representation
of the geometry and physics at the ice shelf/ocean interface is critical to capturing these
dynamics.
We are developing a method for simulating dynamic ice/ocean interaction in a global ocean
model, the Parallel Ocean Program (POP). The interface between ice and ocean can be
represented using stair-steps (partial cells) or using a ghost-cell immersed boundary method
(IBM). In the near future, POP and the Community Ice Sheet Model (CISM) will be coupled
in the Community Earth System Model (CESM); the coupler will handle passing and interpolating fields between models. CISM will dynamically update the geometry of the ice/ocean
interface and POP will supply heat and freshwater fluxes across the interface to CISM. The
partial cells representation of the ice/ocean interface is relatively easy to implement and has
been used to represent ocean bathymetry for more than a decade. The IBM is less proven
but is designed to handle moving boundaries and more accurate in its representation of the
geometry and boundary conditions.
Which physics for coupled ice sheet and ocean models? Lessons learned from
Petermann Glacier
Carl Gladish, New York University, USA
Abstract. Coupling ice sheet and ocean models to investigate their behavior in changing
climate conditions requires careful consideration of the possible physics involved. At the
marine boundaries of the Antarctic and Greenland ice sheets, mass loss due to both iceberg calving and melting is important. Calving, being episodic in time, probably involves
material properties of ice and timescales that are not usually represented in ice sheet models. On the other hand, our numerical simulations of ice shelf melting show that complex
channelized morphology can arise at very small spatial scales in ice shelves that are floating
in relatively warm water. These exploratory simulations were performed using a version of
the Glimmer-CISM ice sheet model coupled to a plume ocean model and the cases studied
were idealizations motivated by Petermann Glacier in Greenland and Pine Island Glacier in
Antarctica. The results of our study of the interplay between melting and ice geometry will
48
Mini-symposia
be presented with an emphasis on principles that could be useful to others working towards
continental scale modeling using coupled, state-of-the-art ice sheet and ocean models. In
particular, we will present results on the important role of ocean mixed-layer physics, the
effect of ocean temperature perturbations on simulated melt rates and also the significance
of sub-glacial discharge of fresh water.
This is a joint work with David Holland (New York University, USA) and Paul Holland
(British Antarctic Survey, Cambridge, UK).
A geometrical multigrid method for shallow ice models based on an energy minimization approach
Guillaume Jouvet, Free University of Berlin, Germany
Abstract. We consider a model for the time evolution of ice sheets and ice shelves that
combines the Shallow Ice Approximation (SIA) for the slow deformation of ice and the Shallow Shelf Approximation (SSA) for the fast basal sliding. At each time step, we have to solve
one scalar generalized p-Laplace problem with obstacle and p > 2 (SIA) and one vectorial
p-Laplace problem with 1 < p < 2 (SSA). Both problems can be advantageously rewritten
by minimising suitable, convex non-smooth energies. By exploiting such formulations, we
implement a fast and robust Newton multigrid method, the convergence being naturally
controlled by the energy. Local non-smoothness are treated by truncation rather than by
regularisation which might affect the solution in an arbitrary way. To update the ice sheet
geometry, we implement the method of characteristics using an recent algorithm of optimal
complexity. In contrast with most of existing numerical models based on finite differences,
our approach has no theoretical restriction on the time-step and allows a wide choice of
unstructured meshes to be used. As an illustration, we present numerical results based on
the exercises of the Marine Ice Sheet Model Inter-comparison Project (MISMIP).
This is a joint work with Ed Bueler (University of Alaska, USA) and Carsten Gräser (Free
University of Berlin, Germany).
Advanced ice sheet modeling: scalable parallel adaptive full Stokes solver and
inversion for basal slipperiness and rheological parameters
Carsten Burstedde, Rheinische Friedrich-Wilhelms-Universitt Bonn, Germany
Omar Ghattas, Tobin Isaac∗ , Noemi Petra, Georg Stadler, and Hongyu Zhu, The
University of Texas at Austin, USA
Abstract. We present a parallel, adaptive mesh, high-order finite element solver for the 3D
full Stokes equations with Glen’s flow law rheology. The adaptive mesh capabilities allow
for efficiently capturing the wide range of length scales with localized features present in
ice sheet dynamics. We solve the equations using a globalized Newton-Krylov method with
block, multilevel preconditioning. We set up realistic calculations using SeaRISE datasets.
Numerical results from these calculations indicate scalability of the algorithm and the implementation for realistic full continent ice sheet simulations.
Additionally, we formulate an inverse problem to infer the basal slipperiness and rheological parameters from surface observations. For this purpose, we minimize the misfit between
observed and modeled surface flow velocities. The resulting least squares minimization problem is solved using an adjoint-based inexact Newton method. Numerical inversion studies
49
Mini-symposia
demonstrate the influence of prior knowledge on the model parameters for addressing illposedness of the inverse problem and to handling noise present in the observations. We
present preliminary work on inverting for basal slipperiness parameters on a continental
scale.
Scalable and composable implicit solvers for polythermal ice flow with steep
topography
Jed Brown, Argonne National Laboratory, USA
Abstract. Ice flow adds additional nonlinearities and a transport-dominated system to
the Stokes problem for ice flow. The heat transport equation has very different spectral
properties from the Stokes system, which preconditioners must respect in order to perform
well. This is achieved using field-split preconditioning composed with geometric and algebraic
multigrid methods. We evaluate the robustness of several preconditioning and nonlinear
solution techniques for the coupled problem and discuss efficient implementation on modern
hardware.
This is a joint work with Matt Knepley (University of Chicago, USA), Dave May (ETH,
Zurich, Switzerland) and Barry Smith (Argonne National Laboratory, USA).
Mini-symposium 4:
Advances in analytical and computational techniques for nonlinear waves
Organizer: Yanzhi Zhang, Missouri University of Science and Technology, USA
Abstract. Recently, research on nonlinear waves has been dramatically expanding and
numerous exciting phenomena have been discovered in this field. This mini-symposium aims
to survey recent advances on various aspects of nonlinear wave studies. The scope of topics
includes the analytical methods and computational techniques used for studying nonlinear
waves, as well as their applications in physical systems.
Analysis of electromagnetic cavity scattering problems
Abstract. In this talk, we consider the scattering of a time-harmonic electromagnetic plane
wave by an open cavity embedded in a perfect electrically conducting infinite ground plane,
where the electromagnetic wave propagation is governed by the Maxwell equations. Given
the incident field, the direct problem is to determine the field distribution from the known
shape of the cavity; while the inverse problem is to determine the shape of the cavity from
the measurement of the field on the open aperture of the cavity. We will discuss both the
direct and inverse scattering problems. The existence and uniqueness of the weak solution
for the direct model problem will be shown by using a variational approach. The perfectly
matched layer method will be investigated to truncate the unbounded electromagnetic cavity
scattering problem. Results on a global uniqueness and a local stability will be presented
for the inverse problem.
Central discontinuous Galerkin methods for shallow water waves
Maojun Li∗ and Liwei Xu, Rensselaer Polytechnic Institute, USA
Abstract. Green-Naghdi equations and standard shallow water wave equations are two
50
Mini-symposia
types of models describing the propagation of shallow water waves. We first develop a
coupling scheme of central discontinuous Galerkin methods and finite element methods for
the solution of Green-Naghdi equations with flat bottom. The numerical scheme is based
on a reduction of the original Green-Naghdi model to a system of hyperbolic equations
together with a stationary elliptic equation. Then, we develop a well-balanced high-order
positivity-preserving central discontinuous Galerkin method solving standard shallow water
wave equations with non-flat bottom. Numerical results will be presented to illustrate the
accuracy and efficiency of the methods.
Global existence for a system of Schrödinger equations with power-type nonlinearities
Nghiem V. Nguyen, Utah State University, USA
Abstract. In this talk, consideration is given to the Cauchy problem for a Schrödinger
system with power-type nonlinearities

m

 i ∂ u + ∆u + X a |u |p |u |p−2 u = 0,
jk k
j
j
j
j
∂t
k=1


uj (x, 0) = ψj 0(x),
(1)
where uj : RN × R → C, ψj0 : RN → C for j = 1, 2, . . . , m and ajk = akj are real numbers. A
sharp form of vector-valued Gagliardo-Nirenberg inequality is first established which yields a
priori estimate needed for global existence of solutions in the sub-critical case, along with the
best embedding constant for the Gagliardo-Nirenberg inequality. Using this best embedding
constant, global existence for small initial data is next shown for the critical exponent case.
The finite time blow-up as well as stability of solution in the critical case are then discussed.
Numerical methods for rotating dipolar BEC based on a rotating Lagrange coordinate
Yanzhi Zhang, Missouri University of Science and Technology, USA
Abstract. In this talk, we discuss an efficient numerical method for simulating the rotating dipolar Bose-Einstein condensates (BEC), which is described by the Gross-Pitaevskii
equation (GPE) with an angular momentum rotation term as well as a dipolar interaction
term. Both terms bring significant difficulties in the analysis and simulations of rotating
dipolar BEC. We apply a rotating Lagrange coordinate to resolve the angular momentum
term; while the dipolar interaction potential is decoupled into local and nonlocal interactions
which results in a Gross-Pitaevskii-Poisson equation. An efficient and accurate numerical
method is introduced to solve the coupled system. Some analytical and numerical results
will be discussed in this talk.
51
Mini-symposia
Mini-symposium 5:
Abstract. Fluid flow problems occur in numerous applications in science and engineering.
Enhancement of physical properties in fluid modeling (such as conservation laws), achievement of long term stability and accuracy of models approximated numerical solutions are
essential. This special session will focus on recent advances in modeling fluid flow dynamics and in numerical methods to compute the approximated solutions of fluid flow models.
Contributions can range from fundamental numerical studies for improvement of models at
continuous and discretized level, and applications to industrial processes. Theoretical and
computational studies based on related physical models are welcome too.
Bayesian source separation in MEG
Daniela Calvetti, Case Western Reserve University, USA
Abstract. Magnetoencephalography (MEG) is a completely non-invasive brain-mapping
modality which uses measurements of the magnetic field outside the head induced by electrical brain activity to localize and characterize the activity inside the brain. Potentially, it
is particularly useful in the study of epilepsy as a tool for localizing the focii of the onset of
seizures. A key issue in MEG is the separation of sources of a different nature. Non-focal
sources from both inside and outside of the brain produce interference, making the inverse
problem of identifying the focal source signal extremely difficult. In this talk we show how
Bayesian methods can be used to address this issue. In particular, we illustrate how a mixed
prior distribution is able to separate sources which are statistically different from each other.
Furthermore, we propose using a depth scan to identify activity from deep focal sources.
Numerical simulations are used to generate controlled data in order to validate the model.
Approximate Deconvolution Large Eddy Simulation of a Barotropic Ocean Circulation Model
Traian Iliescu, Virginia Tech, USA
Abstract. This talk introduces a new large eddy simulation closure modeling strategy for
two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical approximations and does
not employ phenomenological arguments, such as the concept of energy cascade. The new
approximate deconvolution model is tested in the numerical simulation of the wind-driven
circulation in a shallow ocean basin, a standard prototype of more realistic ocean dynamics.
The model employs the barotropic vorticity equation driven by a symmetric double-gyre
wind forcing, which yields a four-gyre circulation in the time mean. The approximate deconvolution model yields the correct four-gyre circulation structure predicted by a direct
numerical simulation, on a much coarser mesh and at a fraction of the computational cost.
This first step in the numerical assessment of the new model shows that approximate deconvolution could represent a viable alternative to standard eddy viscosity parameterizations in
the large eddy simulation of more realistic turbulent geophysical flows.
52
Mini-symposia
Modern ideas in turbulence confront legacy codes
William Layton, University of Pittsburgh, USA
Abstract. The accurate, efficient and reliable simulation of turbulent flows in complex
geometries and modulated by other effects is a recurring challenge. Often these simulations
must be done with legacy codes written a generation of programmers ago. The question
then becomes: How are modern models and methods to be used in such a setting? This
talk will present one path to doing so. The new algorithms involved lead to new models of
turbulence and these lead inevitably to new analysis questions.
Numerical free surface flows on dynamic octree meshes
Maxim Olshanskii, Moscow State University, Russia
Abstract. In the talk, we present an approach for numerical simulation of free surface flows
of viscous Newtonian and viscoplastic incompressible fluids. The approach is based on the
level set method for capturing free surface evolution and features compact finite difference
approximations of fluid and level set equations on locally refined and dynamically adapted
octree cartesian grids. Several important choices have to be made and tools to be developed
for the entire simulations to be predictive and efficient: spacial disretization, time stepping,
handling non-differentiable constitutive relations, surface reconstruction, re-initialization of
the level set function, curvature evaluation, etc. These building blocks will be discussed in
the talk. Numerical examples will demonstrate the performance of the approach for a range
of problems, starting from academic benchmark tests and ending with applications to fluid
animation, catastrophe modelling, and in food industry.
This is a part of the joint research with Kirill Nikitin, Kirill Terehov, and Yuri Vassilevski
from Inst. Numer. Math. RAS in Moscow.
On the Leray regularization with fine mesh filtering
Abigail Bowers, Clemson University, USA
Abstract. We study a numerical method for the Leray-alpha regularization model that
applies the spacial filtering on a finer mesh than is used to resolve the model. Analysis of
this method reveals an optimal scaling between the coarse and fine mesh widths, and the
filtering radius. Moreover, the analysis also shows that polynomials of one lower degree can
be used to resolve the filter problem, making for only a small extra cost associated with the
fine mesh filter solve. Numerical experiments are given that confirm the theory, and show
the effectiveness of the method on benchmark problems.
Dual-mixed finite element methods for the Navier-Stokes equations
Jason Howell, Clarkson University, USA
Abstract. Accurate and efficient numerical methods to approximate fluid flows are important to researchers in many fields, including mechanical, materials, and biomedical engineering. In many applications within these fields, it is of paramount importance to accurately
predict fluid stresses. However, most existing numerical schemes for fluids are formulated
with velocity as the primary unknown of interest, and computation of the fluid stress requires
expensive and potentially inaccurate postprocessing techniques. In this talk, a dual-mixed
variational formulation for the Navier-Stokes equations, in which the stress is a primary
unknown of interest, is derived and analyzed. Using results that provide equivalent sets
53
Mini-symposia
of inf-sup conditions for twofold saddle point problems, it is shown that a finite element
scheme for this method can be constructed from existing schemes for elasticity problems
with weak symmetry of the stress. The extension of this method to non-Newtonian fluids is
also discussed.
An efficient and accurate numerical method for high-dimensional stochastic partial differential equations
Alexander Labovsky, Michigan Technological University, USA
Abstract. The Analysis of Variance (ANOVA) expansion is often used to represent multivariate functions in high dimensions. Using the anchored (Dirac) ANOVA expansion results
in a substantially reduced cost of evaluation of such functions. However, this approach has
two significant flaws. First, the accuracy of the approximation is sensitive to the choice of the
anchor point, which is hard to make a priori. Secondly, when the number of the parameters
is large, the construction of the ANOVA expansion becomes prohibitively expensive. In this
case, efforts were made to recognize which input dimensions have the largest effect upon the
output, and the ANOVA expansion was built using only these important inputs and their
interactions. However, we show that such a simplification can result in a loss of accuracy,
since unimportant inputs often have important interactions. We propose a method for representation of multivariate functions, which does not depend on the choice of the anchor point,
and tracks all the important inputs and important interactions, therefore constructing the
expansion with the exact minimum of the needed terms. We also provide an example of a
real life application where our method is not only computationally attractive, but it is the
only approach capable of approximating the given multivariate function with the expected
accuracy.
Numerical and analytical study for viscoelastic flow in a moving domain
Hyesuk Lee, Clemson University, USA
Abstract. In this talk the problem of a viscoelastic fluid flow in a movable domain is considered. A numerical approximation scheme is developed based on the Arbitrary LagrangianEulerian (ALE) formulation of the flow equations. The spatial discretization is accomplished
by the finite element method, and time-stepping schemes satisfying the geometric conservation law are discussed. We also present some results of viscoelastic flow interacted with an
elastic structure.
Stability and Convergence Analysis: Leray-Iterated-Tikhonov NSE with Time
Relaxation
Abstract. We present a general theory for regularization models of the Navier-Stokes
equations based on the Leray deconvolution model with a general deconvolution operator
designed to fit a few important key properties. We provide examples of this operator, such
as the Tikhonov-Lavrentied and Iterated Tikhonov-Lavrentiev operators, and study their
mathematical properties. An existence theory is derived for the family of models and a
rigorous convergence theory is derived for the resulting algorithms.
54
Mini-symposia
Sensitivity Analysis and Computations for Regularized Navier-Stokes Equations
Monika Neda, University of Nevada Las Vegas, USA
Abstract. We study the sensitivity of the regularized Navier-Stokes equations that are
based on filtering and deconvolution. The sensitivity studies are based on the sensitivity
equation method, where the corresponding differentiation of the model equations is done.
We apply the finite element method to the model and sensitivity equations, and investigate
its algorithm theoretically and computationally.
Linear solvers for incompressible flow simulations using Scott-Vogelius elements
Leo Rebholz, Clemson University, USA
Abstract. We investigate linear solvers for the saddle point linear systems arising in
disc
) Scott-Vogelius finite element implementations of the incompressible Navier((Pk )d , Pk−1
Stokes equations. We discuss the advantages of static condensation applied to these systems
to dramatically reduce the system sizes, and then test direct solvers, several implementations
of augmented Lagrangian preconditioners with GMRES, HLU preconditioned GMRES on
the condensed and uncondensed systems for four test problems.
Analysis of stability and errors of IMEX methods for MHD equations
Hoang Tran, University of Pittsburgh, USA
Abstract. We analyze the stability and accuracy of several implicit-explicit (IMEX) methods for the MHD equations. At small magnetic Reynolds numbers, the methods can be
evolved in time by calls to the NSE and Maxwell codes, each possibly optimized for the
subproblem’s respective physics.
This work is in collaboration with William Layton and Catalin Trenchea
Physics based filtering for the incompressible Leray-α Magnetohydrodynamics
equations
Nicholas Wilson, Clemson University, USA
Abstract. The incompressible magnetohydrodynamics equations (MHD) are derived by
coupling the Navier-Stokes equations (NSE) with Maxwell’s equations. They model fluid
flows in the presence of a magnetic field, when the fluid is electrically conductive but not
magnetic (e.g. salt water). The complexity of these flows do not allow for efficient direct
numerical simulation, which motivates the use of regularization models. The Leray-α MHD
model uses the Helmoholtz filter to remove under resolved scales from the velocity and
magnetic fields. filtered the entire velocity and magnetic fields. To date the velocity and
magnetic fields are filtered entirely. However, recent work for the Leray-α NSE model has
shown that nonlinear filtering that locally chooses the filtering radius based on physics may
improve solutions. We develop physics based criterion for filtering the velocity and magnetic
field for MHD flows, and provide numerical experiments.
The dynamics of two phase complex fluids: drop formation/pinch-off
Xiaofeng Yang, University of South Carolina, USA
Abstract. We present an energetic variational phase-field model for the two-phase incompressible flow with one phase being the nematic liquid crystal. The model leads to a coupled
nonlinear system satisfying an energy law. An efficient and easy-to-implement numerical
55
Mini-symposia
scheme is presented for solving the coupled nonlinear system. We use this scheme to simulate two benchmark experiments: one is the formation of a bead-on-a-string phenomena,
and the other is the dynamics of drop pinching-off. We investigate the detailed dynamical
pinch-off behavior, as well as the formation of the consequent satellite droplets, by varying
order parameters of liquid crystal bulk and interfacial anchoring energy constant. Qualitative
agreements with experimental results are observed.
Mini-symposium #6
Abstract. This mini-symposium is motivated by recent advances on multilevel adaptive
mesh method, multigrid method, domain decomposition method, multiscale method, phase
field/level set method, Newton-Krylov method and their applications on multidimensional,
multiphysics and/or multiphase convection-diffusionreaction problems arising from complex
fluids, fluid-structure coupling, mathematical biology, electromagnetics, renewable energy
(fuel cell, solar cell and battery innovations) and etc. We expect to communicate and discuss
the recent novel techniques/ideas achieved on the modeling and numerical methods about
these topics. More beyond, the related physical models and the corresponding computational
methods will not be limited to aforementioned topics only, any efficient and robust numerical
techniques for solving significant complex systems are welcome to be presented in this session.
An Algebraic Multilevel Preconditioner for Graph Laplacians based on Matching
of Graphs
James Brannick, The Pennsylvania State University, USA
Abstract. We present an algebraic multilevel method for solving Ax = f where A is the
graph Laplacian of an unweighted graph G. We estimate the convergence rate of a two level
method where the coarser level operator is the graph Laplacian of the reduced graph, which
is formed by aggregation where each aggregate contains two or more vertices in the graph
G. We show a general approach of estimating the convergence rate of the corresponding two
level method. Then we constructed a multilevel hierarchy and used Algebraic Multilevel
Iterations (AMLI) in the solving phase. Such combination is proved to have nearly optimal
convergence and time/space complexity on graph Laplacians corresponding to structured
grids, and numerical results indicate good performance on other type of graphs.
This is a joint work with Johannes Kraus (RICAM), and Ludmil Zikatanov (The Pennsylvania State University).
Multigrid Methods for Stokes Equation based on Distributive Gauss-Seidel Relaxation
Long Chen, University of California at Irvine, USA
Abstract. A major difficulty for the numerical simulation of incompressible flows is that
the velocity and the pressure are coupled by the incompressibility constraint. Distributive
56
Mini-symposia
Gauss-Seidel (DGS) relaxation introduced by Achi Brandt and Nathan Dinar is known to be
an efficient decoupled smoothing method for the staggered grid discretization (MAC scheme)
of Stokes equations. In this work, we attempt to design DGS relaxation for discontinuous
pressure finite element approximations of Stokes equations on rectangular grid. We propose
a two-level solver based on DGS smoothing on the fine space and use V-cycle for MAC
scheme as coarse space correction solver. Numerical experiments show that the new solver
achieves the textbook multigrid efficiency.
This is a joint work with Ming Wang (UC Irvine, USA and Peking University, China).
The adaptive nonconforming finite element method for the fourth order problem
Abstract. For the fourth order elliptic problem, most of popular finite element methods
in the literature are the nonconforming finite element method. The partial reason may
lie in that it is actually very difficult to design conforming finite element spaces consisting
of piecewise polynomials. There are a lot of papers concerning a priori analysis of the
nonconforming finite elements in the literature. However, there are few works concerning
the adaptive nonconforming finite element methods of the fourth order problem.
In the first part of the talk, we present the a posteriori error estimator of some nonconforming
elements for the Kirchhoff-Love plate problem. We overcome the key difficulty due to the
lack of proper conforming subspaces and prove that the usual residual-based error estimator
is reliable and efficient for these methods. The main ingredient is the tool used for a prior
error analysis by exploring carefully the continuity condition of these elements.
In the second part of the talk, we address the convergence and optimality of the adaptive
Morley element method for the fourth order elliptic problem. We develop a new technique to
establish a quasi-orthogonality which is crucial for the convergence analysis of the adaptive
nonconforming method. By introducing a new prolongation operator and further establishing
a discrete reliability property, we show the sharp convergence and optimality estimates for
the fourth order elliptic problem.
Algebraic Multigrid Methods for Petroleum Reservoir Simulation
Xiaozhe Hu, The Pennsylvania State University, USA
Abstract. The most time-consuming part of modern Petroleum Reservoir Simulation (PRS)
is solving a sequence of large-scale and ill-conditioned Jacobian systems. In this work, we
develop new effective preconditioners based on Algebraic Multigrid (AMG) Methods for
solving these Jacobian systems. Following the auxiliary space preconditioning framework,
the new preconditioning technique chooses appropriate auxiliary problems according to the
different properties of the equations in the black oil model, and designs robust and efficient
AMG methods for each auxiliary problem. By combining the new preconditioners with
Krylov subspace iterative methods, we construct efficient and robust solvers, which can be
generalized to more complicated models for enhanced oil recovery. Numerical experiments
including preliminary parallel implementations demonstrate the effectiveness and robustness
of our new solvers for PRS.
57
Mini-symposia
Covolume-Upwind Finite Volume Approximations for Linear Elliptic Partial Differential Equations
Lili Ju, University of South Carolina, USA
Abstract. In this talk, we discuss covolume-upwind finite volume methods on rectangular
meshes for solving linear elliptic partial differential equations with mixed boundary conditions. To avoid non-physical numerical oscillations for convection-dominated problems,
nonstandard control volumes (covolumes) are generated based on local Peclet’s numbers and
the upwind principle for finite volume approximations. Two types of discretization schemes
with mass lumping are developed with use of bilinear or biquadratic basis functions as the
trial space respectively. Some stability analyses of the schemes are presented for the model
problem with constant coefficients. Various examples are also carried out to numerically
demonstrate stability and optimal convergence of the proposed methods.
New multigrid methods for the Stokes and linear elasticity problems
Hengguang Li, Wayne State University, USA
Abstract. We have developed new smoothers for the Stokes and linear elasticity problems.
Using the multigrid Poisson solve, we precondition the indefinite system from the finite
element discretization of these saddle point problems. We prove the resulting multigrid
algorithms are contractions with the contraction number depending on the regularity of the
solution but independent of the mesh level.
A treecode elastostatics computation
Hualong Feng, Illinois Institute of Technology, USA
Abstract. We describe an O(N logN) adaptive treecode for elastostatics computation. The
code is tested both with randomly generated data and in a spectrally accurate method for
materials science problems. It is shown that the code scales like O(N logN) asymptotically,
and at the same time fulfills stringent precision requirements prescribed by the spectral
method. We also present a parallelized version of the treecode. The new version is relatively
easier to implement than the previous versions, because it entails less communication between
processors. For non-uniform data, data locality is necessary for load balancing to ensure
speed, and we use the Hilbert curve ordering to implement data locality. We show that
the parallel version scales linearly with the number of processors for both uniform and nonuniform data.
This is a joint work with Shuwang Li, Amlan Barua, and Xiaofan Li.
Operator splitting methods for stiff convection-reaction-diffusion equations
Xingfeng Liu, University of South Carolina, USA
Abstract. Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. Advection-reactiondiffusion equations are traditionally difficult to handle numerically. For reaction-diffusion
systems with both stiff reaction and diffusion terms, implicit integration factor (IIF) method
and its high dimensional analog compact form (cIIF) serve as an efficient class of timestepping methods. For nonlinear hyperbolic equations, front tracking method is one of the
most powerful tools to dynamically track the sharp interfaces. Meanwhile, weighted essentially non-oscillatory (WENO) methods are a class of start-of-the-art schemes with uniform
58
Mini-symposia
high order of accuracy in smooth regions of the solution, which can also resolve the sharp
gradient in accurate and essentially non-oscillatory (ENO) fashion. In this talk, IIF/cIIF
is coupled with front tracking or WENO by the second-order symmetric operator splitting
approach to solve advection-reaction-diffusion equations. In the methods, IIF/cIIF methods treat the stiff reaction-diffusion equations, and front tracking/WENO methods handle
hyperbolic equations that arise from the advection part. In addition, we shall introduce a
method for integrating IIF/cIIF with adaptive mesh refinement (AMR) to take advantage of
the excellent stability condition for IIF/cIIF. The applications of these numerical methods
to fluid mixing and cell signaling will also be presented.
A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion
Systems
Wing-Cheong (Jon) Lo, The Ohio State University, USA
Abstract. An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding
time-dependent reaction-diffusion equations using temporal schemes with a careful choice of
initial condition, which is often estimated through stability analysis. Nonlinear solvers (e.g.
Newton’s method) take less CPU time in direct computing the steady state, however, their
convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematic exploration of spatial patterns of reaction-diffusion
equations under different parameter regimes through numerical simulations requires that the
numerical method be efficient and be robust in terms of initial condition or initial guess, and
it has better likelihood of convergence to inhomogeneous pattern than convergence to spatially constant solutions. In this study, we present a new approach that combines advantage
of temporal schemes in robustness and advantage of Newton’s method in fast convergence in
solving steady states of reaction-diffusion equations. The new iterative procedure is based
on implicit Euler method but without solving the implicit equation exactly at each time
step. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found
to be much more efficient than temporal schemes and to be more robust in convergence than
typical nonlinear solvers (e.g. Newton’s method) in finding the inhomogeneous pattern.
Toward a robust hp-adaptive method for elliptic eigenvalue problems
Jeffrey S. Ovall, University of Kentucky, USA
Abstract. We discuss progress toward a robust hp-adaptive method for approximating
collections of eigenvalues of self-adjoint elliptic operators and their associated invariant subspaces. The robustness is with respect to discontinuities in the coefficients of the differential
operator and the resultant low-regularity of eigenfunctions, as well as the possibility of degenerate or “nearly-degenerate” eigenvalues. Theoretical and computational results of these
authors will be discussed for two hp-adaptive discretizations: one employing a discontinuous
Galerkin approach, with goal-oriented adaptivity designed for these types of problems; the
other using a continuous Galerkin approach, with adaptivity based on an operator-theoretic
approach to a posteriori error analysis, and the use of standard hp-residual error estimates.
It is the latter of these approaches which will be pursued in further research, and indications will be provided of where (and roughly how) improvements are expected in theory and
practice.
59
Mini-symposia
This is a joint work with Luka Grubisic (University of Zagreb, Croatia) and Stefano Giani
(University of Nottingham, United Kingdom).
Dirichlet/Robin iteration-by-subdomain Schwarz-DDM for multiphase fuel cell
model with micro-porous layer
Pengtao Sun, University of Nevada Las Vegas, USA
Abstract. In this talk, an efficient numerical method for a three-dimensional, two-phase
transport model is presented for polymer electrolyte membrane fuel cell (PEMFC) including multi-layer diffusion media, composed of two or more layers of porous materials having
different pore sizes and/or wetting characteristics. Particularly, capillary pressure is continuous, whereas liquid saturation is discontinuous, across the interface of gas diffusion layer
(GDL) and micro-porous layer (MPL), which can improve liquid-water transport in the
porous electrode. We design a nonlinear Dirichlet/Robin iteration-by-subdomain Schwarzdomain decomposition method to deal with water transport in such multi-layer diffusion
media, where Kirchhoff transformation and its inverse techniques are employed to conquer
the discontinuous water diffusivity in the coexisting single- and two-phase regions. In addition, the conservation equations of mass, momentum, charge, hydrogen and oxygen transport
are numerically solved by finite element-upwind finite volume method. Numerical simulations demonstrate that the presented techniques are effective to obtain a fast and convergent
nonlinear iteration for a 3D full PEFC model within around a hundred steps. A series
of numerical convergence tests are carried out to verify the efficiency and accuracy of our
numerical algorithms and techniques.
Cell conservative flux recovery and a posteriori error estimate of high order finite
volume methods
Ming Wang, University of California at Irvine, USA and Peking University, China
Abstract. A cell conservative flux recovery technique is developed for vertex-centered finite
volume methods of second order elliptic equations. It is based on solving a local Neumann
problem on each control volume using mixed finite element methods. The recovered flux is
used to construct a constant free a posteriori error estimator which is proven to be reliable
and efficient. Some numerical tests are presented to confirm the theoretical results.
We emphasize that our method works for general order finite volume methods and the
recovery-based and residual-based a posteriori error estimators is apparently the first results
on a posteriori error estimators for high order finite volume methods.
This is a joint work with Long Chen (UC Irvine, USA).
A parallel geometric-algebraic multigrid solver for the Stokes problem
Chensong Zhang, LSEC, Institute of Computational Mathematics, Chinese Academy of
Sciences, China
Abstract. We propose a scalable parallel solver for the discrete systems from the generalized
Stokes equation discretized by the Taylor-Hood finite element methods. We will analyze a
geometric-algebraic multigrid (GAMG) method for high-order finite element methods for
the Laplacian problem which makes a key ingredient of the preconditioner. We will also
describe details for the parallel implementation and show this algorithm is user-friendly. We
test serial and parallel version of the proposed method with 3D Poisson and Stokes problems
60
Mini-symposia
on unstructured grids; preliminary numerical results show the advantages of the proposed
algorithm.
On a Robin-Robin domain decomposition method with optimal convergence rate
Shangyou Zhang, University of Delaware, USA
Abstract. In this talk, we shall answer a long-standing question: Is it possible that the
convergence rate of the Lions’ Robin-Robin nonoverlapping domain decomposition method is
independent of the mesh size h? The traditional Robin-Robin domain decomposition method
converges at a rate of 1 − O(h1/2 ), even under the optimal parameter. We shall design a
two-parameter Robin-Robin domain decomposition method. It is shown that the new DD
method is optimal, which means the convergence rate is independent of the mesh size h.
A BPX preconditioner for the symmetric discontinuous Galerkin methods on
graded meshes
Liuqiang Zhong, South China Normal University, China and The Chinese University of
Hong Kong, China
Abstract. A multilevel BPX preconditioner for the symmetric discontinuous Galerkin methods on graded meshes is presented. An arbitrary order discontinuous finite element is considered and the resulting preconditioned system is uniformly well conditioned. The theoretical
results are illustrated by numerical experiments.
Adaptive finite element techniques for Einstein constraints
Yunrong Zhu, University of California at San Diego, USA
Abstract. In this talk, we present adaptive finite element approximation techniques for the
constraints arising from the Einstein equations in general relativity. We first derive a priori
L∞ bounds of the discrete solution, without using the restrictive angle condition. Then we
give the adaptive algorithm based on a posteriori error indicator and refinement of simplex
triangulations of the domain, and show that the algorithm converges.
Axially symmetric volume constrained anistropic mean curvature flow
Wenxiang Zhu, Idaho State University, USA
Abstract. We study the long time existence theory for a non local flow associated to a free
boundary problem for a trapped nonliquid drop. The drop has free boundary components
on two horizontal plates and its free energy is anisotropic and axially symmetric. For axially
symmetric intial surfaces with sufficiently large volume, we show the flow exists for all time.
We will also talk about the numerical computations of this flow, especially via the approaches
of front tracking method and the phase field method.
Mini-symposium #7
Statistical methods applied to the inverse problem in electroneurography
Erkki Somersalo, Case Western Reserve University, USA
61
Mini-symposia
Abstract. Electroneurography (ENG) is a method of recording neural activity within
nerves. Using nerve electrodes with multiple contacts the activation patterns of individual neuronal fascicles can be estimated by measuring the surface voltages induced by the
intraneural activity. The information about neuronal activation can be used for functional
electric stimulation (FES) of patients suffering of spinal chord injury, or to control a robotic
prosthetic limb of an amputee. However, the ENG signal estimation is a severely ill-posed
inverse problem due to uncertainties in the model, low resolution due to limitations of the
data, geometric constraints, and the difficulty to separate the signal from biological and
exogenous noise. In this article, a reduced computational model for the forward problem is
proposed, and the ENG problem is addressed by using beamformer techniques. It is shown
that the beamformer algorithm can be interpreted as a version of the classical Backus-Gilbert
algorithm. Furthermore, we show that using a hierarchical statistical model, it is possible
to develop an adaptive beamformer algorithm that estimates directly the source variances
rather than the voltage source itself. The advantage of this new algorithm, e.g., over a traditional adaptive beamformer algorithms is that it allows a very stable noise reduction by
averaging over a time window. In addition, a new projection technique for separating sources
and reducing cross-talk between different fascicle signals is proposed. The algorithms are
tested on a computer model of realistic nerve geometry and time series signals.
An Efficient and Stable Spectral Method for Electromagnetic Scattering from a
Layered Periodic Structure
Ying He - Purdue University, USA
Abstract. The scattering of acoustic and electromagnetic waves by periodic structures plays
an important role in a wide range of problems of scientific and technological interest. This
contribution focuses upon the stable and high order numerical simulation of the interaction
of time harmonic electromagnetic waves incident upon a periodic doubly layered dielectric
media with sharp, irregular interface. We describe a Boundary Perturbation Method for
this problem which avoids not only the need for specialized quadrature rules but also the
dense linear systems characteristic of Boundary Integral/Element Methods. Additionally,
it is a provably stable algorithm as opposed to other Boundary Perturbation approaches
such as Bruno & Reitich’s Method of Field Expansions” or Milder’s Method of Operator
Expansions.” Our spectrally accurate approach is a natural extension of the Method of
Transformed Field Expansions” originally described by Nicholls & Reitich (and later rened
to other geometries by the authors) in the single layer case.
A Schwarz generalized eigen-oscillation spectral element method (GeSEM) for
2-D high frequency electromagnetic scattering in dispersive inhomogeneous media
Xia Ji, LSEC, Institute of Computational Mathematics, Chinese Academy of Sciences,
China
Abstract. In this paper, we propose a parallel Schwarz generalized eigen-oscillation spectral element method (GeSEM) for 2-D complex Helmholtz equations in high frequency wave
scattering in dispersive inhomogeneous media. This method is based on the spectral expansion of complex generalized eigen-oscillations for the electromagnetic fields and the Schwarz
non-overlapping domain decomposition iteration method. The GeSEM takes advantages
62
Mini-symposia
of a special real orthogonality property of the complex eigen-oscillations and a new radiation interface condition for the system of equations for the spectral expansion coefficients.
Numerical results validate the high resolution and the flexibility of the method for various
materials.
Sparse reconstruction in diffuse optical tomography
Taufiquar Rahman Khan, Clemson University, USA
Abstract. In this talk, a short overview of the basics of image reconstructio n in diffuse
optical tomography (DOT) will be presented. Extension of the distinguish-ability criteria of
Isaacson and Knowles to opti mal source in DOT will be discussed. A sparsity constrained
reconstruction problem in DOT for determining the optical parameters from bou ndary
measurements will be presented. The sparsity of the inclusion with resp ect to a particular
basis is assumed a priori. The proposed approach is based on a sparsity promoting l1-penalty
term similar to the approach of Jin et al. for electrical impedance tomography [Journal of
Inverse and Ill-Posed Problems].
An eigenvalue method using multiple frequency data
Jiguang Sun, Delaware State University, USA
Abstract. Dirichlet and transmission eigenvalues have important applications in qualitative
methods in inverse scattering. Motivated by the fact that these eigenvalues can be obtained
from scattering data, we propose a new eigenvalue method using multiple frequency data
(EM2 F). The method detects eigenvalues and builds indicator functions to reconstruct the
support of the target. Numerical reconstruction is quite satisfactory. Estimation of Dirichlet
or transmission eigenvalues is obtained. Furthermore, reconstruction of D and estimation
of eigenvalues can be combined together to distinguish between the sound soft obstacle and
non-absorbing inhomogeneous medium.
Mini-symposium #8
Abstract. The exploitation of computable a posteriori error bounds within adaptive meshrefinement strategies is of fundamental importance to guarantee the reliable and efficient
numerical simulation of mathematical models arising in computational science and engineering. The objective of this minisymposium is to present recent work undertaken in this
field; in particular, topics of interest will include: dual-weighted-residual error estimation,
adaptive model reduction, error estimation of time-dependent problems, and hp-adaptive
refinement strategies.
Adaptive Model Reduction for Coupled Thermoelastic Problems
Mats Larson, Umeå University, Sweden
Abstract. In this contribution we develop adaptive model reduction for coupled thermoelastic problems.The adaptive method is based on a discrete a posteriori error estimate for
63
Mini-symposia
a thermoelastic model problem discretized using a reduced finite element method. We first
consider the case when the problem is one-way coupled in the sense that heat transfer affects
elastic deformation, but not vice versa. Then we extend our analysis to the fully coupled
case with temperature dependent material parameters. A reduced model is constructed using component mode synthesis (CMS) in each of the heat transfer and linear elastic finite
element solvers. The error estimate bounds the difference between the reduced and the standard finite element solution in terms of discrete residuals and corresponding dual weights.
A main feature with the estimate is that it automatically gives a quantitative measure of
the propagation of error between the solvers with respect to a certain computational goal.
Based on the estimates we design adaptive algorithms that enable automatic tuning of the
number of modes required in each substructure. The analytical results are accompanied by
numerical examples.
This is a joint work with H. Jakobsson (Umeå University).
Two-Grid hp–Adaptive Discontinuous Galerkin Finite Element Methods for Second–
Order Quasilinear Elliptic PDEs
Abstract. In this talk we present an overview of some recent developments concerning
the a posteriori error analysis and adaptive mesh design of h– and hp–version discontinuous
Galerkin finite element methods for the numerical approximation of second–order quasilinear
elliptic boundary value problems. In particular, we consider the derivation of computable
bounds on the error measured in terms of an appropriate (mesh–dependent) energy norm
in the case when a two-grid approximation is employed. In this setting, the fully nonlinear problem is first computed on a coarse finite element space VH,P . The resulting ‘coarse’
numerical solution is then exploited to provide the necessary data needed to linearise the
underlying discretization on the finer space Vh,p ; thereby, only a linear system of equations
is solved on the richer space Vh,p . Here, an adaptive hp–refinement algorithm is proposed
which automatically selects the local mesh size and local polynomial degrees on both the
coarse and fine spaces VH,P and Vh,p , respectively. Numerical experiments confirming the
reliability and efficiency of the proposed mesh refinement algorithm are presented.
Advanced Aspects of Adaptive Higher-Order Methods
Lukas Korous, Charles University, Prague
Abstract. In this presentation we give a survey of our recent results in adaptive hp-FEM and
hp-DG methods. The presentation has four parts. In part 1 we illustrate the importance of
fully anisotropic hp refinements and present a new suite of benchmark problems that can be
used to assess anisotropic capabilities of adaptive hp-FEM codes. In part 2 we present a novel
PDE-independent hp-adaptive multimesh discretization method for multiphysics coupled
problems. In contrast to operator-splitting methods, our approach preserves the coupling
structure of all physical fields on the discrete level, which results into better accuracy and
stability of the approximation. In part 3 we mention a monolithic multimesh discretization
of problems involving compressible inviscid flow where the flow part is discretized using hpDG and second-order equations are discretized using hp-FEM. In part 4 we introduce the
Hermes library for rapid development of space- and space-time adaptive hp-FEM and hp-DG
solvers.
64
Mini-symposia
Adaptive Higher-Order Finite Element Methods for Transient PDE Problems
Based on Embedded Higher-Order Implicit Runge-Kutta Methods
Pavel Solin, University of Nevada, Reno, USA
Abstract. We present a new class of adaptivity algorithms for time-dependent partial
differential equations (PDE) that combine adaptive higher-order finite elements (hp-FEM)
in space with arbitrary (embedded, higher-order, implicit) Runge-Kutta methods in time.
Weak formulation is only created for the stationary residual, and the Runge-Kutta methods
are specified via their Butcher’s tables. Around 30 Butcher’s tables for various RungeKutta methods with numerically verified orders of local and global truncation errors are
provided. A time-dependent benchmark problem with known exact solution that contains
a sharp moving front is introduced, and it is used to compare the quality of seven embedded implicit higher-order Runge-Kutta methods. Numerical experiments also include a
comparison of adaptive low-order FEM and hp-FEM with dynamically changing meshes.
All numerical results presented in this paper were obtained using the open source library
Hermes (http://hpfem.org/hermes) and they are reproducible in the Networked Computing
Laboratory (NCLab) at http://nclab.com.
This is a joint work with Lukas Korous (Charles University, Prague, Czech Republic).
Blockwise Adaptivity for Time Dependent Problems Based on Coarse Scale Adjoint Solutions
August Johansson, University of California, Berkeley, USA
Abstract. We describe and test an adaptive algorithm for evolution problems that employs
a sequence of ”blocks” consisting of fixed, though nonuniform, space meshes. This approach
offers the advantages of adaptive mesh refinement but with reduced overhead costs. A key
issue with a block adaptive approach is determining block discretizations from coarse scale
solution information that achieve the desired accuracy. We describe several strategies for
achieving this goal using adjoint-based a posteriori error estimates, and we demonstrate the
behaviour of the proposed algorithms in various examples, such as a coupled PDE-ODE
system.
A Posteriori Error Estimation via Nonlinear Error Transport
Jeff Banks, Lawrence Livermore National Laboratory, USA
Abstract. Error estimation for time dependent hyperbolic problems is challenging for theoretical and practical reasons. In these systems, error can propagate long distances and
produces effects far from the point of generation. In addition, nonlinear interactions of error, as well as nonlinear discretizations can play important roles and should be addressed.
In this talk we investigate the use of error equations for a posteriori error estimation. We
extend the existing work using linear error transport equations, and discuss situations where
the this approach is found to be deficient. In particular, we investigate the effects of nonlinearities in the error equations, which are particularly important for situations where local
errors become large such as near captured shocks. The auxiliary PDEs are treated numerically to yield field estimates of error and we discuss subtleties associated with the numerical
treatment of the nonlinear error transport equations.
Dual Problems in Error Estimation and Uncertainty Propagation for Hyperbolic
Problems
65
Mini-symposia
Tim Barth, NASA Ames Research Center Moffett Field, USA
Abstract. Dual problems arise in a number of computational settings including a-posteriori
error estimation, mesh adaptivity, sensitivity analysis, uncertainty propagation, and optimization. Even so, computational demands placed on the dual problem may differ significantly for each computational setting. We have developed a general software framework
for error estimation, solution adaptivity, and uncertainty propagation. This software framework been successfully applied to numerical computations of compressible Navier-Stokes
flow, hypersonic Navier-Stokes flow with finite-rate chemistry, magnetohydrodynamics, and
Euler-Maxwell flow. In this presentation, we will discuss this software framework, show
computational applications for hyperbolic problems, and discuss outstanding problems and
future challenges.
A Posteriori Error Estimation for Compressible Flows using Entropy Viscosity
Murtazo Nazarov∗ , Jean-Luc Guermond, Bojan Popov, Texas A&M University, USA
Abstract. We present a goal-oriented adaptive finite element method for the compressible
Euler/Navier-Stokes equations using continuous Galerkin finite elements. The mesh adaption
relies on a duality-based a posteriori error estimation of the output functional. We derive
a posteriori error estimations of the quantity of interest in terms of a dual problem for the
linearized Euler equations. The primal and the dual problems are solved by using an entropy
based artificial viscosity method which we call entropy viscosity. The numerical viscosity
is proportional to the entropy residual in the primal problem and proportional to the dual
residual in the dual problem. Both problems are solved using continuous piecewise linear
finite elements in space and explicit Runge-Kutta methods in time. The implementation in
two and three space dimensions as well as different boundary conditions are discussed. A
number of benchmark problems are solved to validate the performance of the method.
Mini-symposium #9
Estimating the bias of local polynomial approximation methods using the Peano
kernel
Jerome Blair*, Keystone International and NSTec, USA
Abstract. The determination of uncertainty of an estimate requires both the variance and
the bias of the estimate. Calculating the variance of local polynomial approximation (LPA)
estimates is straightforward. We present a method, using the Peano kernel, to estimate the
bias of LPA estimates and show how this can be used to optimize the LPA parameters in
terms of the bias-variance tradeoff. Figures of merit are derived and values calculated for
several common methods.
66
Mini-symposia
Hybrid Numerical Techniques for Efficient Determination of stochastic Nonlinear Dynamic Responses via harmonic Wavelets
P.D. Spanos, Rice University, USA
Abstract. Responses of dynamical systems exposed to stochastic excitations described by
harmonic wavelets are considered. A surrogate optimal linear system is introduced which facilitates the nonlinear system response. The surrogate system is determined by satisfying an
appropriate error minimization criterion. Subsequently the convenient spectral input/output
relationship of the surrogate system are utilized to compute the spectrum of the stochastic
response of the nonlinear system.Results from extensive numerical studies demonstrate the
reliability and efficiency of the proposed method.
Computational Methods for Analyzing Fluid Flow Dynamics from Digital Imagery
Aaron Luttman, National Security Technologies LLC, USA
Abstract. Optical flow is the term used to describe the inverse problem of extracting
physical flow information from time-dependent image data. The classical variational methods are based on the assumption of conservation of intensity, which is only appropriate for
divergence-free and non-advective flows. We present a method for analyzing fluid flows from
digital imagery, by adapting the classical variational approach for computing dense flows,
which incorporates the physics of fluid flows into the data fidelity and allows for a variety
of prior assumptions on the flow, through the regularization. The computed flow fields are
then used to analyze the flow dynamics, using methods from computational dynamical systems. The method is demonstrated on synthetic data as well as on data-assimilated, model
imagery of sea surface temperature of the Columbia River delta in Oregon, USA.
This is a joint work with Erik Bollt, Ranil Basnayake, and Sean Kramer.
Application of Random Field Theory
A.V. Balakkrishnan, University of California, Los Angeles, USA
Abstract. 2D and 3D random field models: Turbulence-the Kolmogorov Theory: Aeroelastic Flutter; Monitoring Wind Flow by Laser Foreward Scattering; NonLinear Noise Functionals.
Analysis and Methods for Time Resolved Neutron Detection
Neveen Shlayan, Singapore-MIT Alliance for Research & Technology, USA
Abstract. Various aspects of the neutron spectroscopy problem have been studied. Theoretically, the neutron emission problem is parallel to the limited angle radon transform
problem. In order to solve this ill posed problem, various algorithms were developed spanning two different techniques; algebraic reconstruction as well as Monte-Carlo methods. The
developed algorithms are the Stochastic Gradient Approximation (SGA) method, Simultaneous Perturbation Stochastic Approximation (SPSA) method, and Time of Flight (TOF)
method. Enhanced adaptive techniques were developed as well in order to improve the
current methods.
67
Mini-symposia
Stochastic Spectral Approximation with Redundant Multiresolution Dictionaries for Uncertainty Quantification
Daniele Schiavazzi∗ and Gianluca Iaccarino, Stanford University, USA
Abstract. The possibilities related to the quantification of the aleatoric uncertainty of physical systems have greatly increased in recent years. Many reliable methodologies are already
available in the literature to efficiently propagate the uncertainty from input quantities to
system responses. The present work focuses on non intrusive methodologies in which one
deterministic simulation is required for every realization. As a consequence, all propagation
schemes aim at reducing the total number of samples, while preserving the maximum possible
accuracy in the response statistics. While various methods have been recently proposed, two
main challenges remain to be tackled. One is related to problems in which a large number
of random parameters or a small correlation length of stochastic processes involved lead to
very high dimensions in random space. The second challenge is the presence of discontinuities in stochastic space commonly observed in problems involving instability or bifurcation
phenomena. The present work proposes a novel framework assembled with the above challenges in mind. Responses are represented in a multiresolution Alpert multiwavelet basis
dictionary, where piecewise smooth responses exhibit a sparse structure. Furthermore, this
non intrusive framework offers a straightforward generalization of Legendre and Haar chaos
techniques, allowing both polynomial fitting in large domain areas together with the ability
of capturing discontinuous responses. Stochastic spectral coefficients are evaluated using
greedy methodologies within the Compressed Sensing paradigm, in an attempt to unveil
the intrinsic redundancy in the response, of special interest for increasing dimensionality.
In particular, a sparse tree representation in the Alpert multiwavelet domain is assumed,
to improve the reconstruction of the stochastic response. The effect of various sampling
strategies is also investigated to provide better reconstruction performances.
Conservation Law Methods for Uncertainty Propagation in Dynamic Systems
Lillian Ratliff, UC Berkeley, USA
Abstract. We present methods of propagating uncertainty in the initial condition through
various types of dynamical systems with the goal of gaining insights into the geometric
representation of the uncertainty as it evolves under the dynamics. In particular, we provide
a review of uncertainty propagation in systems of ordinary differential equations. Using this
as motivation, we present a method for propagating uncertainty in systems with parametric
uncertainty. We construct probability spaces at each time step and define an evolution
operator which is preserves the probability measure. We also propose a method to extend
these result to dynamical systems characterized by differential inclusions.
68
Other Talks
High Order Finite Difference Methods for Maxwell’s Equations in Dispersive
Media
Vrushali Bokil, Oregon State University, USA
Abstract. We consider models for electromagnetic wave propagation in linear dispersive
media which include ordinary differential equations for the electric polarization coupled to
Maxwell’s equations. We discretize these models using high order finite difference methods
and study the properties of the corresponding discrete models. In this talk we will present
the stability, dispersion and convergence analysis for a class of finite difference methods
that are second order accurate in time and have arbitrary (even) order accuracy in space.
Using representative numerical values for the physical parameters, we validate the stability
criterion while quantifying numerical dissipation. Lastly, we demonstrate the effect that the
spatial discretization order and the corresponding stability condition has on the dispersion
error.
HDG methods for Reissner-Mindlin plates
Fatih Celiker, Wayne State University, USA
Abstract. We introduce a family of hybridizable discontinuous Galerkin (HDG) methods
for solving the Reissner-Mindlin plate equations. The method is based on rewriting the equations a system of first-order partial differential equations. We then introduce the hybridized
method which results in the elimination of all the unknowns except for those associated with
the transverse displacement and rotations of the vertical fibers at the edges of the mesh.
Therefore, the methods are efficiently implementable. We prove that the methods are welldefined and display numerical results to ascertain their convergence behavior. We also show
numerically that a simple element-by-element post-processing of the transverse displacement
provides an approximation which converges faster than the original approximation.
Spectral Collocation Methods for Volterra Integro-Differential Equations
Yanping Chen, South China Normal University, China
Abstract. This talk presents Legendre spectral collocation methods for pantograph Volterra
delay-integro-differential equations and Jacobi spectral collocation methods for weakly singular Volterra integro-differential equations with smooth solutions and with nonsmooth solutions in some special case. We provide a rigorous error analysis for the spectral methods,
which shows that both the errors of approximate solutions and the errors of approximate
derivatives of the solutions decay exponentially in L∞ -norm and weighted L2 -norm. The
numerical examples are given to illustrate the theoretical results.
Multi-frequency methods for an inverse source problem
S. Acosta, Rice University, USA
S. Chow∗ , Brigham Young University, USA
V. Villamizar, Brigham Young University, USA
Abstract. We study an inverse source problem in acoustics, where an unknown source is to
be identified from the knowledge of its radiated wave. The existence of non-radiating sources
at a given frequency leads to the lack of uniqueness for the inverse source problem. In our
69
Other Talks
previous work we prove that data obtained from finitely many frequencies is not sufficient.
On the other hand, if the frequency varies within an open interval of the positive real line,
then the source is determined uniquely. We will discuss two algorithms for the reconstruction
of the source using multi-frequency data. One algorithm is based on an incomplete Fourier
transform of the measured data and we establish an error estimate under certain regularity
assumptions on the source function. The other algorithm involves the solution of an adjoint
problem. Some numerical result will be presented.
Generalized image charge solvation model for electrostatic interactions in molecular dynamics simulations of aqueous solutions
Shaozhong Deng, UNC Charlotte, USA
Abstract. I will discuss the extension of the image charge solvation model (ICSM) [J. Chem.
Phys. 131, 154103 (2009)], a hybrid explicit/implicit method to treat electrostatic interactions in computer simulations of bio- molecules formulated for spherical cavities, to prolate
spheroidal and triaxial ellipsoidal cavities, designed to better accommodate non-spherical
solutes in molecular dynamics (MD) simulations. In addition to the utilization of a general
truncated octahedron as the MD simulation box, central to the proposed extension is the
computation of reaction fields in an one-image approximation for non-spherical objects. The
resulting generalized image charge solvation model (GICSM) is tested in simulations of liquid water, and the results are analyzed in comparison with those obtained from the ICSM
simulations as a reference.
L2 Projected C 0 Elements for non H 1 Very Weak Solution of curl and div Operators
Huoyuan Duan, Nankai University, China
Abstract. Most partial differential equations either are governed by curl and div operators or can be recast into the ones governed by curl and div operators. Note that
−∆u = curlcurlu − ∇divu. In general, a well-known fact for curl and div operators the
solution is non H 1 very weak solution, although curl and div operators are closely related to
gradient operator. The non H 1 solution may be caused by many reasons, such as interfacial
corners, cross-points, reentrant corners, reentrant edges, irregular boundary points, singular
right-hand side and boundary data (e.g., Dirac, L1 data), and so on. An intractable difficulty has been well-known for more than half a century that the classical continuous C 0 finite
element method fails in seeking a correct convergent finite element solution for the non H 1
space very weak solution. In particular, more badly, the classical continuous C 0 finite element method of the relevant eigenproblem is seriously polluted by spurious solutions. What
is pessimistically worse, when applied to the classical continuous C 0 finite element method,
the adaptive finite element method is useless for non H 1 very weak solution of curl and div
operators, although the adaptive method has been pervasively well-known to be so strong
and so powerful in dealing singularities in scientific and engineering computations. In this
talk we shall report our work [1] on how to generalize and adapt and apply our L2 projected
C 0 finite element method (continuous/H 1 -conforming) [2] for a vectorial second-order elliptic
eigenvalue problem in the form of the curlcurl-grad div operator, where the eigenfunctions
may be very weak and may not be in H 1 space. Such eigenproblems usually arise from
computational electromagnetism and computational fluid-structure interaction problem. In
70
Other Talks
[1] we show that optimal error bounds O(h2r ) are obtained for eigenvalues for the non H 1
space eigenfunctions with the H r regularity for some 0 < r < 1, and that our L2 projected
C 0 finite element method is spectrally correct.
Acknowledgements This work was supported in part by the National Natural Science
Foundation of CHINA under the grants 11071132 and 11171168 and the Research Fund for
the Doctoral Program of Higher Education of China under grant 20100031110002.
References
[1] H. Y. Duan, P. Lin and R.C.E Tan: Error estimates for a vectorial second-order elliptic
eigenproblem by the local L2 projected C 0 finite element method, research report.
[2] H. Y. Duan, F. Jia, P. Lin, and R.C.E. Tan: The local L2 projected C 0 finite element
method for Maxwell problem, SIAM J. Numer. Anal., 47(2009), pp. 1274–1303.
On A Family of Models in X-ray Dark-field Tomography
Weimin Han, University of Iowa, USA
Abstract. X-ray mammography is currently the most prevalent imaging modality for screening and diagnosis of breast cancers. However, its success is limited by the poor contrast
between healthy and diseased tissues in the mammogram. A potentially prominent imaging
modality is based on the significant difference of x-ray scattering behaviors between tumor
and normal tissues. Driven by major practical needs for better x-ray imaging, exploration
into contrast mechanisms other than attenuation has been active for decades, e.g., in terms
of scattering, which is also known as dark-field tomography. In this talk, a theoretical study
is provided for the x-ray dark-field tomography (XDT) assuming the spectral x-ray detection
technology.
The radiative transfer equation (RTE) is usually employed to describe the light propagation
within biological medium. It is challenging to solve RTE numerically due to its integrodifferential form and high dimension. For highly forward-peaked media, it is even more
difficult to solve RTE since accurate numerical solutions require a high resolution of the
direction variable, leading to prohibitively large amount of computations. For this reason,
various approximations of RTE have been proposed in the literature. For XDT, a family
of differential approximations of the RTE is employed to describe the light propagation for
highly forward-peaked medium with small but sufficient amount of large-angle scattering.
The forward and inverse parameter problems are studied theoretically and approximated
numerically.
Instant System Availability
Kai Huang∗ and Jie Mi, Florida International University, USA
Abstract. In this work, we study the instant availability A(t) of a repairable system through
integral equation. We proved initial monotonicity of availability, and derived lower bounds
to A(t) and average availability. The availabilities of two systems are compared. Numerical
algorithm for computing A(t) is proposed. Examples show high accuracy and efficiency of
this algorithm.
71
Other Talks
Optimization Under Uncertainty: Models and Computational Techniques
Ralph Baker Kearfott, University of Louisiana at Lafayette, USA
Abstract. In various situations, some quantities or model parameters are not known precisely, but may be known to lie within certain bounds, while other quantities that affect
outcomes are under our control. We wish to compute the best possible outcome under these
conditions. Mathematically, we have an objective function φ, a set of controllable parameters
x, and a set of unknown parameters u, and we wish to solve the problem
min φ(x, u)
x
(2)
where x ∈ x ∈ Rn , u ∈ u ∈ Rp , where we may choose the values x, but where the values u
are unknown and out of our control. Here, we may assume x and u are hyperrectangles, and
we may also have additional equality or inequality constraints involving both the x’s and u’s.
There are several interpretations of what solutions to such an imprecisely known problem
are, and each interpretation leads to its own computational issues. In this talk, we give an
overview of common ways of defining the solution to (2), mention the appropriateness of
each in real-world situations, and discuss computational difficulties and advantages of each.
A Scalable Non-Conformal Domain Decomposition Method For Solving TimeHarmonic Maxwell Equations In 3D
Z. Peng∗ and J. F. Lee, Ohio State University, USA
Abstract. We present a non-overlapping and non-conformal domain decomposition method
(DDM) for solving the time-harmonic Maxwell equations in R3. There are three major technical ingredients in the proposed non-conformal DDM: a. A true second order transmission
condition (SOTC) to enforce fields continuities across domain interfaces; b. A corner edge
penalty term to account for corner edges between neighboring sub-domains; and, c. A global
plane wave deflation technique to further improve the convergence of DDM for electrically
large problems. It is shown previously that a SOTC, which involves two second-order transverse derivatives, facilitates convergence in the conformal domain decomposition method for
both propagating and evanescent electromagnetic waves across domain interfaces. However,
the discontinuous nature of the cement variables across the corner edges between neighboring sub-domains remains troublesome. To mitigate the technical difficulty encountered
and to enforce the needed divergence-free condition, we introduced a corner edge penalty
term into the interior penalty formulation for the non-conformal DDM. The introduction of
the corner edge penalty term successfully restored the superior performance of the SOTC.
Finally, through an analysis of the DDM with the SOTC, we show that there still exists a
weakly convergent region where the convergence in the DDM can still be unbearably slow
for electrically large problems. Furthermore, it is found that the weakly convergent region is
centered at the cutoff modes, or electromagnetic waves propagate in parallel to the domain
interfaces. Subsequently, a global plane wave deflation technique is utilized to derive an
effective global-coarse-grid preconditioner to promote fast convergence of the cutoff or near
cutoff modes in the vicinity of domain interfaces.
72
Other Talks
Generalized Foldy-Lax Formulation and its Application to the Inverse Scattering
Abstract. We consider the scattering of a time-harmonic plane wave incident on a twoscale hetero-geneous medium, which consists of scatterers that are much smaller than the
wavelength and extended scatterers that are comparable to the wavelength. A generalized
Foldy-Lax formulation is proposed to capture multiple scattering among point scatterers
and extended scatterers. Our formulation is given as a coupled system, which combines the
original Foldy–Lax formulation for the point scatterers and the regular boundary integral
equation for the extended obstacle scatterers. An efficient physically motivated Gauss-Seidel
iterative method is proposed to solve the coupled system, where only a linear system of
algebraic equations for point scatterers or a boundary integral equation for a single extended
obstacle scatterer is required to solve at each step of iteration. In contrast to the standard
inverse obstacle scattering problem, the proposed inverse scattering problem is not only to
determine the shape of the extended obstacle scatterer but also to locate the point scatterers.
Based on the generalized Foldy–Lax formulation and the singular value decomposition of the
response matrix constructed from the far-field pattern, an imaging function is developed to
visualize the location of the point scatterers and the shape of the extended obstacle scatterer.
A Multiple-Endpoints Chebysheve Collocation Method For High Order Problems
Shan Wang and Zhiping Li∗ , Peking University, China
Abstract. Pseudospectral methods as meshless methods are successfully used for widely
diverse applications. The Chebyshev type collocation methods are among the most popular spectral methods because of computational convenience. A typical choice of collocation
points for solving boundary value problems of second order differential equations with a
Chebyshev method is to use the Chebyshev-Gauss-Lobatto collocation points, which include certain inner collocation points and two end points. Chebyshev-Gauss collocation
method, which has no endpoints, is also a popular choice. However, difficulties, such as overdetermined system or ill-conditioned differential matrix, often arise when pseudospectral
method is applied to higher order differential equations, especially in high dimensions.
In this paper, following the idea of establishing the Gauss-Lobatto collocation points, we
design a new type of collocation points, named multiple-endpoints collocation points for
high order differential equations. Simply speaking, for problems with K boundary conditions
on each boundary points, a sequence of orthogonal polynomials is established in such a
way that each polynomial in the sequence has, other than the separated inner zeros, the
boundary points as its K-zeros, and the collocation points are then determined in a standard
way. Numerical examples on 1D 6th-order and 2D 4th-order linear differential equations,
with both hard clamped boundary condition and reciprocally periodic connection boundary
conditions, are presented to show the improved condition numbers of the differential matrices
and accuracy of the new method as compared with the method using Gauss and GaussLobatto collocation points. In particular, we present an example on an elastic thin film
buckling problem governed by a nonlinear von Karman equation, for which the standard
Chebyshev methods failed to produce physically consistent solutions
73
Other Talks
Hybrid weighted essentially non-oscillatory schemes with different indicators
Jianxian Qiu∗ , Xiamen University, China
Gang Li, Qingdao University, China
Abstract. A key idea in finite difference weighted essentially non-oscillatory (WENO)
schemes is a combination of lower order fluxes to obtain a higher order approximation. The
choice of the weight to each candidate stencil, which is a nonlinear function of the grid values,
is crucial to the success of WENO. For the system case, WENO schemes are based on local
characteristic decompositions and flux splitting to avoid spurious oscillatory. But the cost of
computation of nonlinear weights and local characteristic decompositions is very expensive.
In the presentation, we investigate hybrid schemes of WENO schemes with high order upwind linear schemes using different discontinuity indicators and explore the possibility in
avoiding the local characteristic decompositions and the nonlinear weights for part of the
procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong shocks. The idea is to identify discontinuity by an discontinuity indicator,
then reconstruct numerical flux by WENO approximation at discontinuity and up-wind linear approximation at smoothness. These indicators are mainly based on the troubled-cell
indicators for discontinuous Galerkin (DG) method which are listed in the paper by Qiu
and Shu {SIAM J. Sci. Comput. 27 (2005) 995-1013}. The emphasis of the paper is on
comparison of the performance of hybrid scheme using different indicators, with an objective
of obtaining efficient and reliable indicators to obtain better performance of hybrid scheme
to save computational cost. Detail numerical studies in one- and two-dimensional cases are
performed, addressing the issues of efficiency (less CPU time and more accurate numerical
solution), non-oscillatory property.
A High-Order Transport Scheme for Unstructured Atmosphere and Ocean Climate Models
Todd Ringler∗ and Robert Lowrie, Los Alamos National Laboratory, USA
Abstract. Traditional climate models of the atmosphere and ocean have utilized latitudelongitude meshes or, more recently, quasi-uniform, structured meshes. A joint project between NCAR and LANL has recently resulted in global atmosphere and ocean climate models
that are able to utilize variable resolution, unstructured, conforming meshes. These models
allow for the placement of enhanced resolution in specific areas of interest, such as over North
America for the atmosphere and in the North Atlantic for the ocean. Tessellating the surface
of the sphere with an arbitrary set of conforming, convex polygons presents many numerical
challenges, not the least of which is the development of high-order transport schemes.
To start, we will briefly summarize this new modeling system, called Model for Prediction
Across Scales, and present global atmosphere and ocean simulations that have been conducted to date. We will then turn quickly to the topic of transport. First, we will motivate
the importance of accurate and conservative transport in climate system models. We will
then present an extension of the Characteristic Discontinuous Galerkin transport method
suitable for arbitrary convex polygon meshes. The method retains an arbitrary number of
basis functions per element (i.e. per convex polygon). Fluxes across element faces are computed by tracking fluid velocities backward in time to determine the volume swept across
each face during the time step. The flux of tracer constituents is computed by integrating
74
Other Talks
the swept region with high-order quadrature. Boundedness of tracer values is insured during
the computation of the fluxes across each face.
Examples of the impact of this high-order transport scheme will be presented for an idealized
configuration of the Antarctic Circumpolar Current.
A mixed finite element method with exactly divergence-free velocities for incompressible magnetohydrodynamics
Dominik Schoetzau, University of British Columbia, Canada
Abstract. We propose and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem, in two and three
dimensions. The velocity field is discretized using divergence-conforming Brezzi-DouglasMarini (BDM) elements and the magnetic field is approximated by curl-conforming Nedelec
elements. The conformity of the velocity field is enforced by a discontinuous Galerkin approach. A central feature of the method is that it produces exactly divergence-free velocity
approximations, and captures the strongest magnetic singularities. We prove that the energy norm error is convergent in the mesh size in general Lipschitz polyhedra under minimal
regularity assumptions, and derive nearly optimal a-priori error estimates. We present a comprehensive set of numerical experiments, which indicate optimal convergence of the proposed
method for two-dimensional as well as three-dimensional problems.
Networked Computing Laboratory (NCLab)
Pavel Solin∗ and Lukas Korous, University of Nevada – Reno, USA
Academy of Sciences of the Czech Republic, Czech Republic
Charles University, Prague, Czech Republic
Petr Mach, Czech Technical University, Czech Republic
Abstract. The Networked Computing Laboratory (NCLab) is a pioneering web framework
for collaborative scientific computing, as well as a new vehicle for the transfer of knowledge
between academia and the public. NCLab has different objectives from commercial softwares
such as Matlab, Maple, MathCAD, Comsol, Ansys and others. As part of its objectives it
provides a mechanism for researchers to develop interactive graphical applications based
on their own computational methods, and make them instantly available to vast amounts
of users. NCLab is powered by cloud computers and it works entirely in the web browser
window. It uses advanced networking technologies to provide a highly creative atmosphere of
sharing and real-time collaboration. Users can (obviously) access their accounts on anytimeanywhere basis, including from mobile devices, meet in NCLab and work there together. The
only requirement is a working Internet connection. The framework is still in development,
but it already has around 1000 regular users. In this presentation we will describe basic
features of NCLab and focus on modules for geometrical modeling, mesh generation, and
postprocessing that can be attached to any finite element code that complies with their
simple APIs. We will also mention directions for NCLab’s future development.
75
Other Talks
A balanced finite element method for singularly perturbed reaction-diffusion
problems
M. Stynes∗ , National University of Ireland, Ireland
Runchang Lin, Texas A&M International University, USA
Abstract. An introduction is given to the properties of the singularly perturbed linear
reaction-diffusion problem −2 ∆u+bu = f posed in Ω ⊂ Rd , with the homogeneous Dirichlet
condition u = 0 on ∂Ω, where d ≥ 1, the domain Ω is bounded with (when d ≥ 2) Lipschitzcontinuous boundary ∂Ω, and the parameter satisfies 0 < 1. These properties reveal
that for this type of problem, the standard associated energy norm v 7→ [2 |v|21 + kvk20 ]1/2 is
too weak a norm to measure adequately the errors in solutions computed by finite element
methods because the exponent of ε in this norm is too large so that the norm is essentially
equivalent to the L2 norm.
This failure is because the norm is unbalanced: its different components have different orders
of magnitude. A balanced and stronger norm is introduced, then for d ≥ 2 a mixed finite
element method is constructed whose solution is quasi-optimal in this new norm. By a
duality argument it is shown that this solution attains a higher order of convergence in the
L2 norm. Error bounds derived from these analyses are presented for the cases d = 2, 3. For
a problem posed on the unit square in R2 , an error bound that is uniform in ε is derived
when the new method is implemented on a Shishkin mesh.
Pricing Options under Jump-diffusion Models
Jari Toivanen, Stanford University, Stanford, USA
Abstract. The value of assets like stocks usually have more complicated behavior than a
geometric Brownian motion assumed by the Black-Scholes model. For example, sometimes
the value has jump-like rapid change. European options can be exercised only when they
expire while American options can be exercised any time during their life. Often it is possible
to derive a formula for the price of a European option while usually American options need
to be priced using numerical methods.
When jumps are included in the model, a parabolic partial integro-differential equation can
be derived for the price of a European option. For the price of an American option, a linear
complementarity problem with the same operator can be derived. We design and analyze
efficient numerical methods for pricing options using finite difference discretizations. Particularly, we consider the treatment of the integral terms due to the jumps. We demonstrate
that sufficiently accurate prices for most practical purposes can be computed in a small
fraction of a second on a PC.
Multiphase complex fluid models and their applications to complex biological
systems
Qi Wang, University of South Carolina, USA
Abstract. I will present a multiphase complex fluid models for a number of complex fluid
phases along with their interfacial boundaries. Interfacial elasticity in some interfaces can be
enforced and so can the long range molecular interaction within some phases. The model is
then applied to study cell cluster aggregate fusion and cytoskeletal dynamics and buffer-cell
interaction leading to cell migration.
76
Other Talks
Topics on electromagnetic scattering from cavities
Aihua W. Wood, Air Force Institute of Technology, USA
Abstract. The analysis of the electromagnetic scattering phenomenon induced by cavities
embedded in an infinite ground plane is of high interest to the engineering community.
Applications include the design of cavity-backed conformal antennas for civil and military
use, the characterization of radar cross section (RCS) of vehicles with grooves, and the
advancement of automatic target recognition. Due to the wide range of applications and
the challenge of solutions, the problem has been the focus of much mathematical research in
recent years.
This talk will provide a survey of mathematical research in this area. In addition I will
describe the underlining mathematical formulation for this framework. Specifically, one
seeks to determine the fields scattered by a cavity upon a given incident wave. The general
way of approach involves decomposing the entire solution domain to two subdomains via an
artificial boundary enclosing the cavity: the infinite upper half plane over the infinite ground
plane exterior to the boundary, and the cavity plus the interior region. The problem is solved
exactly in the infinite sub-domain, while the other is solved numerically. The two regions
are then coupled over the artificial boundary via the introduction of a boundary operator
exploiting the field continuity over material interfaces. We will touch on both the Perfect
Electric Conducting and Impedance ground planes. Results of numerical implementations
will be presented.
Most Likely Paths of Shortfalls in Long-Term Hedging with Short-Term Futures
Zhijian Wu, University of Alabama, USA
Abstract. With or without the constraint of the terminal risk, an optimal strategy to
minimize the running risk in hedging a long-term commitment with short-term futures can
be solved explicitly if the underline stock follows the simple stochastic differential equation
dSt = µdt + σdBt
where Bt is the standard Brownian motion. In this talk, the most likely paths of shortfalls
associated with the hedging are discussed. We typically focus on the shortfalls corresponding to the optimal strategies established to minimize the running risk with or without the
terminal constraint. These paths give information about how risky events occur and not just
their probability of occurrence.
Mortar multiscale methods for Stokes-Darcy flows in irregular domains
Ivan Yotov, University of Pittsburgh, USA
Abstract. We study multiscale numerical approximations for the coupled Stokes-Darcy flow
system. The equations in the coarse Darcy elements (or subdomains) are discretized on a fine
grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite
differences on irregular grids. The Stokes subdomains can be discretized by any stable Stokes
finite elements. The subdomain grids do not have to match across the interfaces. Continuity
conditions between coarse elements are imposed via a mortar finite element space on a coarse
grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive
optimal order convergence on the fine scale for the multiscale pressure and velocity. The
77
Other Talks
algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale
mortar interface problem that is solved using a multiscale flux basis. Numerical experiments
are presented to confirm the theory and illustrate the efficiency and flexibility of the method.
The talk is based on joint work with Benjamin Ganis, Vivette Girault, Pu Song, and Danail
Vassilev
Fractional Differential Equations: Modeling and Numerical Solutions
Chuanju Xu, Xiamen University, China
Abstract. The fractional partial differential equations are extensions of the traditional
models, based on fractional calculus. They are now winning more and more scientific applications cross a variety of fields including control theory, biology, electrochemical processes,
viscoelastic materials, polymer, finance, and etc. In this talk, we will address the fractional
models using random walk process, and numerical methods to solve these models. Particularly, we focus on the existence and uniqueness of the weak solution, and its spectral
approximations. Two definitions, i.e. Riemann–Liouville definition and Caputo one, of the
fractional derivative are considered in parallel. We construct and analyze efficient spectral
approximations based on the weak formulations associated to these two definitions. Some
interesting applications to viscoelastic materials and molecular biology will also be discussed.
Direct Discontinuous Galerkin method and Its Variations for Diffusion Problems
Jue Yan∗ and Chad Vidden, Iowa State University, USA
Abstract. In this talk, we will discuss the recent four discontinuous Galerkin methods
for diffusion problems; 1) the Direct discontinuous Galerkin(DDG) method; 2) the DDG
method with interface corrections; 3) the DDG method with symmetric structure; and 4) a
new DG method with none symmetric structure. Major contribution of the DDG method is
the introduction of the jumps of second or higher order solution derivatives in the numerical
flux formula. The symmetric version of the DDG method helps us obtain the optimal L2(L2)
error analysis for the DG solution. For the non-symmetric version, we show that the scheme
performs better than the Baumann-Oden scheme or the NIPG method in the sense that
optimal order of accurcy is recovered with even-th order polynomial approximations. A
series of numerical examples are presented to show the high order accuracy and the capacity
of the methods. At the end, we will discuss the recent studies of the maximum-principlesatisfying or the positivity preserving properties of the DDG related methods.
High order interface methods for electromagnetic systems in dispersive inhomogeneous media
Shan Zhao, University of Alabama, USA
Abstract. Across a material interface separating two dielectric media, the electromagnetic
fields are known to be non-smooth or even discontinuous. Moreover, if one dielectric medium
is dispersive, such a discontinuity will be frequency-dependent or time-varying. Based on
the auxiliary differential equation (ADE) approach, we will examine such a dispersive interface problem with the Debye dispersion model. A novel mathematical formulation will
be established to describe the regularity changes in electromagnetic fields at the dispersive
interface. The resulting time-dependent jump conditions will then be numerically enforced
via the matched interface and boundary (MIB) scheme. Some preliminary numerical results
78
Other Talks
will be reported.
Sponsors: NSF (DMS-0616704, DMS-0731503, and DMS-1016579) and University of Alabama RGC Award.
Second Order Virtual Node Algorithms for Stokes Flow Problems with Interfacial Forces and Irregular Domains
Diego C. Assêncio∗ and Joseph M. Teran, University of California, Los Angeles, USA
Abstract. We present numerical methods for the solution of the Stokes equations in irregular domains and with interfacial discontinuities. We handle both the continuous and
discontinuous viscosity cases. In both of them, our method provides discretely divergence
free velocities which are second order accurate. The discretization is performed on a uniform
MAC-grid employing virtual nodes at interfaces and boundaries. Interfaces and boundaries
are represented with a hybrid Lagrangian/level set method. The discretizations of both
the irregular domain and the interface problem with continuous viscosity yield symmetric
positive definite linear systems, while the discretization of the interface problem with discontinuous viscosity yields a symmetric indefinite linear system. Numerical results indicate
second order accuracy in L∞ .
A Fast Volume Integral Solver for 3-D Objects Embedded in Layered Media
Min Hyung Cho∗ and Wei Cai, The University of North Carolina at Charlotte, USA
Abstract. The Helmholtz equation is solved for 3-D objects embedded in layered media.
The layered media Green’s function is found in two steps. First, the spectral Green’s function
is obtained with a transfer matrix technique. Then, the Sommerfeld integral is numerically
taken to obtain the real space Green’s function. The surface pole effects and slow decay of
the spectral Green’s function in the Sommerfeld integral are addressed with the adaptive
generalized Gaussian quadrature rules and the window function, respectively. The efficiency
of the two numerical techniques will be presented. Next, by rewriting the Helmholtz integral
operator in layered media as a summation of 2-D cylindrical wave operators, a parallel fast
solver is developed. Here, the 2-D cylindrical wave operators are calculated independently
with a wideband Fast Multipole Method or a local expansion tree-code in a fast manner.
The fast solver is implemented with OpenMP for a shared memory machine and compared
with the direct solver. With the layered media Green’s function, a volume integral equation is derived and implemented for cube objects embedded in a layered structure by using
appropriate interface and decay conditions and Green’s 2nd identity.
Unconditionally Positive Residual Distribution Schemes for Hyperbolic Conservation Laws
M.E.Hubbard∗ and D.Sármány,University of Leeds, UK
M.Ricchiuto, INRIA Bordeaux, France
Abstract. The residual distribution framework was developed as an alternative to the finite
volume approach for approximating hyperbolic systems of conservation laws which would allow a natural representation of genuinely multidimensional flow features. The resulting
algorithms are closely related to conforming finite elements, but their structure makes it far
simpler to construct nonlinear approximation schemes, and therefore to avoid unphysical
79
Other Talks
oscillations in the numerical solution. They have been successfully applied to a wide range
of nonlinear systems of equations, producing accurate simulations of both steady and, more
recently, time-dependent flows. When designed carefully, these schemes have the following
very useful properties.
• They can be simultaneously second order accurate (in space and time) and free of
unphysical oscillations, even in the presence of turning points in the solution.
• The CRD (Conservative Residual Distribution) formulation [1] provides a very natural
way to approximate balance terms in a manner which automatically retains equilbria
inherent in the underlying system.
• It is possible to construct residual distribution schemes which allow for a discontinuous
representation of the dependent variables [2]. In particular, the inclusion of discontinuities in time allows for the development of schemes which are unconditionally positive
[3], i.e. they are free of unphysical oscillations whatever size of time-step is taken. Discontinuities in space provide a very natural manner in which to approximate shocks
and to apply weak boundary conditions.
This presentation will focus on discontinuous residual distribution and the development
of unconditionally positive schemes for approximating multidimensional, time-dependent
problems. The combination of second order accuracy and unconditional positivity will be
demonstrated for the scalar advection equation, followed by a discussion of recent progress
on their extension to nonlinear systems of equations. Numerical results will be presented
for the Euler equations and/or the shallow water equations. For the latter, the issue of
constructing a well-balanced scheme for the case where source terms are used to represent
variable bed topography will be addressed.
References
[1] A.Csik, M.Ricchiuto, H.Deconinck, J Comput Phys, 179(2):286–312, 2002.
[2] M.E.Hubbard, J Comput Phys, 227(24):10125–10147, 2008.
[3] M.E.Hubbard, M.Ricchiuto, Comput Fluids, 46(1):263–269, 2011.
Lie Group Analysis – a microscope of physical and engineering sciences
Ranis N. Ibragimov, University of Texas at Brownsville, USA
Abstract. The formulation of fundamental natural laws and of technological problems in
the form of rigorous mathematical models is given frequently, even prevalently, in terms of
nonlinear differential equations. An appropriate method for tackling nonlinear differential
equations is provided by Lie group analysis.
The aim of this presentation is, from the one hand, to impart to the wide audience of
researchers and students with the comprehensive and easy to follow introduction to Lie’s
group analysis and, from the other hand, is to present several recent results in this area
whose discussion discloses the advantages to be gained from the use of the group theoretic
approach.
The emphasis will be on an application of Lie group analysis to fully nonlinear Navier-Stokes
equations modelling the large-scale atmospheric motion around the rotating Earth. The
80
Other Talks
inquiry is motivated by dynamically significant Coriolis forces in meteorology and oceanographic applications such as a climate variability models and the general atmospheric circulation. This project is aimed to contribute to a better observational knowledge of the
spatial and temporal distribution of mixing in the atmosphere and the ocean than achieved
to date. Application of Lie group analysis allows to perform the complete integration of the
model by quadratures and thus to write the exact solutions of the Navier-Stokes equations in
terms of elementary functions and visualize them. One of the impacts of the project is, from
one hand, to learn more about the influences of large scale fluid flows on the environment,
highlighted by fundamental issues such as global warming and long term climate change and,
from the other hands, is to illustrate the advantages of mathematical modeling of e.g., oil
spill associated with the Deepwater Horizon incident.
Partially, the presentation is based on the research projects that also involve a graduate
student:
References
Ibragimov, R.N., Dameron, M., 2011: Spinning phenomena and energetics of spherically
pulsating patterns in stratified fluids. Physica Scripta, 84, 015402.
Ibragimov, R.N., Pelinovsky, D.E., 2010: Effects of rotation on stability of viscous stationary
flows on a spherical surface. Physics of Fluids, 22, 126-602
On Generalized Bell Numbers for Complex Argument
Roberto B. Corcino∗ , Maribeth B. Montero, Mindanao State University, Philippines
Cristina B. Corcino, De La Salle University, Philippines
Abstract. In this talk, more properties of the generalized Bell numbers and polynomials
for integral arguments are obtained. Moreover, the generalized Stirling numbers of the
second kind for complex arguments are defined using Hankel contour and some properties
necessary in defining and investigating the generalized Bell numbers for complex argument
are established.
Asymptotic Formulas for the Generalized Stirling Numbers of the Second Kind
with Integer Parameters
Cristina B. Corcino∗ , De La Salle University, Philippines
Nestor G. Acala and Jay M. Ontolan, Mindanao State University, Philippines
Abstract. Asymptotic formulas of the classical Stirling numbers have been done by many
authors like Temme [Studies in Applied Math., Vol.89 (1993)] and Moser and Wyman [Duke
Math, Vol.25, 29-43, (1958)] due to the importance of the formulas in computing values of
the numbers under consideration when parameters become large. The generalized Stirling
numbers on the other hand, are important due to their statistical applications [Matimyas
Matematika Vol.25(1) 19–29 (2002) ]. The generalization of Stirling numbers considered
here are generalizations along the lines of Hsu and Shuie’s unified generalization [Advances
in Appl. Math. Vol.20 366-384 (1998)] and R. B. Corcino’s generalization [Mindanao Forum,
Vol. XIV, no.2, 91-99 (1999)]. In this paper two asymptotic formulas for the generalized
Stirling numbers of the second kind with integer parameters are obtained and the range of
validity of each formula is established.
81
Other Talks
A Potential-based Finite Element Scheme with CGM for Eddy Current Problems
Tong Kang, Communication University of China, China
Abstract. An improved potential-based nodal finite element scheme combining with Composite Grid Method (CGM) is used to solve 3D eddy current problems. In our scheme,
introducing a magnetic vector potential and an electric scalar potential is justified as a
better way of dealing with possible discontinuities of coefficients. By appending a penalty
function to the potential-based formulation, the existence and uniqueness of approximating
solutions are ensured. Some computer simulations of the magnetic flux density and eddy current density for two eddy current benchmark models (TEAM Workshop Problem 7 and IEEJ
model) are demonstrated to verify the feasibility and efficiency of the proposed algorithms.
Discontinuous-in-Space Explicit Runge-Kutta Residual Distribution Schemes for
Hyperbolic Conservation Laws
M. E. Hubbard, University of Leeds, UK
M. Ricchiuto, Inria Bordeaux, France
A. Warzyński∗ , University of Leeds, UK
Abstract. The Residual Distribution (RD) framework for multidimensional hyperbolic con¯
servation laws can be illustrated by considering the scalar conservation law given by
∇·f =0
(3)
on a domain Ω, with appropriate boundary conditions. The residual associated with a mesh
cell E is defined to be
Z
φE =
∇ · f dΩ,
(4)
E
and this is then distributed among the vertices of E. Assuming a piecewise linear representation of the approximate solution leads to the discrete system
X
βiE φE = 0
∀i
(5)
E∈Di
where the βiE signify the proportion of the residual in cell E assigned to node i and Di
denotes the subset of triangles containing i. System (5) is solved to find the approximate
solution values at the mesh nodes, typically using a pseudo-time-stepping approach.
In the case of steady state problems, where f in (3) only has a spatial dependence, the RD
concept has already proven to be very successful. The RD approach, in a relatively natural
manner, enables construction of positive, linearity preserving and conservative schemes able
to carry out a truly multidimensional upwinding for both scalar and systems of hyperbolic
conservation laws.
Extension to time-dependent problems is currently a subject of intensive ongoing research.
It is possible to develop schemes of the form (5), as derived when the divergence in (3)
includes the time variation, but solving the system (5) at each time-step is typically very
cpu-intensive. To overcome this Abgrall and Ricchiuto in [1] proposed a framework for
explicit, second order residual distribution schemes for transient problems. In this talk I will
82
Other Talks
present their approach in conjunction with discontinuous-in-space data representation. This
extends previous work on discontinuous residual distribution schemes for steady problems
initiated in [2, 3]. It also extends work of Abgrall and Shu [4] in the sense that it reformulates
the Runge-Kutta Discontinuous Galerkin (DG) method in the framework of Runge-Kutta
RD schemes. This is, briefly speaking, done by considering flux differences (edge residuals
in the RD framework) instead of the fluxes themselves.
Different types of cell– and edge–based distribution strategies can be applied and we will
discuss the most interesting choices characteristic for either RD [2, 3] or DG type approaches
[4, 5]. Relevant numerical results for two-dimensional hyperbolic conservation laws will be
presented and available analytical results discussed. We will also briefly comment on other
recent developments in the discontinuous RD framework, i.e. discontinuous-in-time schemes
[6], and compare our approach with possible alternatives like DG schemes [5].
References
[1] R. Abgrall, M. Ricchiuto Explicit Runge–Kutta residual distribution schemes for
time dependent problems: second order case. J. Comput. Phys. 229(16), 5653–5691, 2010.
[2] M. E. Hubbard A framework for discontinuous fluctuation distribution. Internat. J.
Numer. Methods Fluids 56(8), 1305–1311, 2008.
[3] M. E. Hubbard Discontinuous fluctuation distribution. J. Comput. Phys. 227(24),
10125–10147, 2008.
[4] R. Abgrall, C.-W. Shu Development of Residual Distribution Schemes for the Discontinuous Galerkin Method: The Scalar Case with Linear Elements. Commun. in Comp.
Phys. 5(2), 376-390, 2009.
[5] B. Cockburn, S.-C. Hou, C.-W. Shu The Runge–Kutta local projection discontinuous Galerkin finite-element method for conservation laws. 4 The Multidimensional Case.
Mathematics of Computation 54(190), 545-581, 1990.
[6] M. E. Hubbard, M. Ricchiuto Discontinuous upwind residual distribution: A route
to unconditional positivity and high order accuracy. Comput. Fluids, Volume 46, Issue 1,
2011.
Effects of Rotation on Energy Stabilization of Internal Gravity Waves Confined
in a Cylindrical Basin
Michael Dameron, University of Texas at Brownsville, USA.
Abstract. A linear, uniformly stratified ocean model is used to investigate propagation of
large scale internal gravity waves confined in a cylindrical basin. Because of the inclusion of
significant Coriolis acceleration and stable stratification, the presence of vertical boundaries
allows one to associate the wave motion under question with baroclinic Kelvin waves. A
particular question of interest was to investigate the effects of rotation on energetics of Kelvin
waves. It was found that the Earth’s rotation stabilizes the energy density fluctuation as well
as pressure perturbation of Kelvin waves. We also observe the existence of the rotationally
persistent oceanic region where the energy density changes relatively rapidly with the depth.
The time series of the equipotential curves for the energy density were visualized as spinning
patterns that look rotating in an anticlockwise sense when looking from above the North
83
Other Talks
Pole. Such spinning patterns were compared with the flow around a low-pressure area that
is usually being linked with a modeling of hurricanes. Discussion of nonlinear modeling is
also presented.
Dispersion and Dissipation Analysis of Two Fully Discrete Discontinuous Galerkin
Methods
He Yang∗ , Rensselaer Polytechnic Institute, USA
Fengyan Li, Rensselaer Polytechnic Institute, USA
Jianqian Qiu, Nanjing University, China
Abstract. The dispersion and dissipation properties of numerical methods are very important in wave simulations. In this talk, such properties will be analyzed for Runge-Kutta
and Lax-Wendroff discontinuous Galerkin methods when solving the linear advection equation. With the standard method of calculating discrete dispersion relation, it will be shown
that the dispersion and dissipation errors of these two numerical schemes are of the same
order of accuracy, but with different leading coefficients. For Lax-Wendroff discontinuous
Galerkin methods, an alternative approach is introduced and shown to have some advantage
in computing discrete dispersion relation. By making use of this approach, how to construct
better numerical flux is also discussed. Small time step limit is considered for both RungeKutta and Lax-Wendroff discontinuous Galerkin methods. The role of temporal and spatial
discretization in discrete dispersion relation is eventually clarified.
Higher and Approximate Symmetries of Differential Equations Using MAPLE
Grace Jefferson, Deakin University, Australia
Abstract. One method of finding special exact solutions of differential equations is afforded
by the work of nineteenth century mathematician Sophus Lie (1842-1899) and the use of continuous transformation groups. In recent times, there has been an ever increasing interest in
higher symmetries, that is, symmetries which have a dependence on derivatives of dependent
variables. The automated determination of these higher symmetries, through the generation
and solution of a determining system of equations using computer algebra systems, leads
us to describe the MAPLE computer algebra package DESOLVII (Vu, Jefferson and Carminati 2011), which is a major upgrade of DESOLV (Vu and Carminati 2003). DESOLVII
now includes new routines allowing the determination of higher symmetries (contact and
Lie-Bcklund) for systems of both ordinary and partial differential equations. In the brief
comparative study carried out, DESOLVII was found to be the only package (of three) to
find all full solution sets for both point and higher symmetries in fast times.
Moreover, extensions to the basic Lie group theory have also been proposed. Of particular
interest here is the theory of approximate symmetries which deals fundamentally with a combination of perturbation theory and classical Lie group analysis. A recent paper compared
three methods of determining approximate symmetries of differential equations. Two of these
methods are well known and involve either a perturbation of the classical Lie symmetry generator of the differential system (Baikov, Gazizov and Ibragimov 1988) or a perturbation of
the dependent variable/s and subsequent determination of the classical Lie symmetries of
the resulting coupled system (Fushchich and Shtelen 1989), both up to a specified order in
the perturbation parameter. The third method, proposed by Pakdemirli, Yrsoy and Dolapi
(2004), simplifies the calculations required by Fushchich and Shtelen’s method through the
84
assignment of arbitrary functions to the non-linear components prior to computing symmetries.
All three methods have been implemented in the new MAPLE package ASP (Automated
Symmetry Package), an add-on to DESOLVII. The algorithms for each of the three methods
have been implemented and tested, allowing the efficient computation of approximate symmetries for differential systems. In addition, the results obtained from this study highlighted
the ability of ASP to find more generalised functions which extend approximate algebras
using a classification routine and an altered PDE solution routine. To our knowledge, it
is now the only package currently available in MAPLE which is able to find approximate
symmetries by all three methods.
Immerse Finite Element Methods for Solving Parabolic Type Moving Interface
Problems
Xu Zhang, Virginia Tech, USA
Abstract. In science and engineering, many simulations are carried out over domains consisting of multiple materials separated by curves/surfaces. This often leads to the so-called
interface problems of partial differential equations whose coefficients are piecewise constants.
Using conventional finite element methods, convergence cannot be guaranteed unless meshes
are constructed according to the material interfaces. Due to this reason the mesh in a conventional finite element method for solving an interface problem has to be unstructured to
handle non- trivial interface configurations. This restriction usually causes many negative
impacts on the simulations if material interfaces evolve. In this presentation, we will discuss
how the recently developed immersed finite elements (IFE) can alleviate this limitation of
conventional finite element methods. We will present both semi-discrete and full discrete IFE
methods for solving parabolic equations whose diffusion coefficient is discontinuous across a
time dependent interface. We will also use IFEs in method of lines (MoL) to obtain another
class of flexible, efficient, and reliable methods for solving parabolic moving interface problems. These methods can use a fixed structured mesh even the interface moves. Numerical
examples will be provided to demonstrate features of these IFE methods.
85
86
Name
Walter Allegretto
Todd Arbogast
Xylar Asay-Davis
Diego C. Assêncio
A.V. Balakkrishnan
Randolph E. Bank
Jeff Banks
Gang Bao
Tim Barth
John Berger
B. Bialecki
Jerome Blair
Pavel Bochev
Vrushali Bokil
Yassine Boubendir
Abigail Bowers
James Brannick
Sean Breckling
Jed Brown
Jiacheng Cai
Xiao-Chuan Cai
Daniela Calvetti
Liqun Cao
Fatih Celiker
Raymond Chan
Qingshan Chen
Zhangxin Chen
C.S. Chen
Long Chen
Yanping Chen
Yitung Chen
Min Hyung Cho
Sum Chow
Cristina B. Corcino
Roberto B. Corcino
Michael Dameron
Leszek Demkowicz
Institution
University of Alberta, Canada
University of Texas at Austin, USA
Los Alamos National Laboratory, USA
University of California, Los Angeles, USA
University of California, Los Angeles, USA
University of California at San Diego, USA
Lawrence Livermore National Laboratory, USA
Zhejiang University, China and
Michigan State University, USA
NASA Ames Research Center Moffett Field, USA
Colorado School of Mines, USA
Colorado School of Mines, USA
Keystone International and NSTec, USA
Sandia National Laboratories, USA
Oregon State University, USA
New Jersey Institute of Technology, USA
Clemson University, USA
The Pennsylvania State University, USA
University of Nevada, Las Vegas, USA
Argonne National Laboratory, USA
University of Colorado at Boulder, USA
Case Western Reserve University, USA
Chinese Academy of Sciences, China
Wayne State University, USA
The Chinese University of Hong Kong, Hong Kong
University of Calgary, Canada
University of Southern Mississippi, USA
University of California at Irvine, USA
South China Normal University, China
The University of North Carolina at Charlotte, USA
Brigham Young University, USA
De La Salle University, Philippines
Mindanao State University, Philippines
University of Texas at Brownsville, USA
ICES, UT Austin, USA
87
Name
Shaozhong Deng
Huoyuan Duan
Derrick Dubose
Katherine J. Evans
Graeme Fairweather
Hualong Feng
R. I. Fernandes
Carl Gladish
Max Gunzburger
Weimin Han
Ying He
Jan S Hesthaven
Robert L. Higdon
Paul Houston
Jason Howell
Xiaozhe Hu
Jun Hu
Kai Huang
Matthew Hubbard
Ranis N. Ibragimov
Traian Iliescu
Tobin Isaac
hline Grace Jefferson
E.W. Jenkins
Xia Ji
August Johansson
Guillaume Jouvet
Lili Ju
Tong Kang
Andreas Karageorghis
Ralph Baker Kearfott
Pushkin Kachroo
Taufiquar Rahman Khan
Lukas Korous
Alexander Labovsky
Mats Larson
William Layton
Hyesuk Lee
Wei Leng
Peijun Li
Hengguang Li
Zhiping Li
Jichun Li
Institution
UNC Charlotte, USA
Nankai University, China
Oak Ridge National Laboratory, USA
American Mathematical Society, USA
Illinois Institute of Technology, USA
The Petroleum Institute, UAE
New York University, USA
Florida State University, USA
University of Iowa, USA
Purdue University, USA
Brown University, USA
Oregon State University, USA
University of Nottingham, UK
Clarkson University, USA
The Pennsylvania State University, USA
Peking University, China
Florida International University, USA
University of Leeds, UK
University of Texas at Brownsville, USA
Virginia Tech, USA
The University of Texas at Austin, USA
Deakin University, Australia
University of California, Berkeley, USA
Free University of Berlin, Germany
University of South Carolina, USA
Communication University of China, China
University of Cyprus, Cyprus
University of Louisiana at Lafayette, USA
Charles University, Prague
Michigan Technological University, USA
University of Umea, Sweden
University of Pittsburgh, USA
Purdue University, USA
Peking University, China
88
Name
Wenyuan Liao
Yanping Lin
Xingfeng Liu
Wing-Cheong (Jon) Lo
Aaron Luttman
Eric Machorro
Carolina Manica
Daniel Martin
Michael McCourt
Peter Minev
Chiara Mocenni
Paul Muir
Ram Nair
Murtazo Nazarov
Monika Neda
Nghiem V. Nguyen
Maxim Olshanskii
Jeffrey S. Ovall
Duccio Papini
Zhen Peng
Mauro Perego
Jianxian Qiu
Lillian Ratliff
Leo Rebholz
Todd Ringler
Antoine Rousseau
Daniele Schiavazzi
Dominik Schoetzau
Helene Seroussi
Qin Sheng
Neveen Shlayan
Chi-Wang Shu
Leslie Smith
Pavel Solin
Erkki Somersalo
P.D. Spanos
Martin Stynes
Jiguang Sun
Pengtao Sun
Weiwei Sun
Shuyu Sun
Institution
University of Calgary, Canada
The Hong Kong Polytechnic University, Hong Kong
The Ohio State University, USA
National Security Technologies LLC, USA
National Security Technologies, LLC, USA
Universidade Federal do Rio Grande do Sul, Brasil
Lawrence Berkeley National Lab, USA
Cornell University, USA
University of Alberta, Edmonton, Canada
University of Siena, Italy
Saint Marys University, Canada
National Center for Atmospheric Research, USA
Texas A&M University, USA
Utah State University, USA
Moscow State University, Russia
University of Kentucky, USA
Università degli Studi di Siena, Italy
Ohio State University, USA
Florida State University, USA
Xiamen University, China
UC Berkeley, USA
INRIA, France
Stanford University, USA
University of British Columbia, Canada
Caltech-Jet Propulsion Laboratory, USA and
Ecole Centrale Paris, Chatenay-Malabry, France
Baylor University, USA
Singapore-MIT Alliance for Research & Technology, USA
Brown University, USA
University of Wisconsin, Madison, USA
University of Nevada, Reno, USA
Case Western Reserve University, USA
Rice University, USA
National University of Ireland, Ireland
Delaware State University, USA
City University of Hong Kong, Hong Kong
KAUST, Kingdom of Saudi Arabia
89
Name
Xudong Sun
Yuzhou Sun
Mark Taylor
Jari Toivanen
Hoang Tran
Jiajia Wang
Qi Wang
Ming Wang
A. Warzyński
Mary F. Wheeler
Nicholas Wilson
Yau Shu Wong
Aihua W. Wood
Zhijian Wu
Hong Xie
Liwei Xu
Jinchao Xu
Chuanju Xu
Guangri Xue
Jue Yan
Xiaofeng Yang
He Yang
Hongtao Yang
Ivan Yotov
Yanzhi Zhang
Shuhua Zhang
Zhimin Zhang
Xu Zhang
Chensong Zhang
Shangyou Zhang
Shan Zhao
Liuqiang Zhong
Jiang Zhu
Wenxiang Zhu
Yunrong Zhu
Institution
Sandia National Laboratory, USA
Stanford University, Stanford, USA
UC Irvine, USA and Peking University, China
University of Leeds, UK
The University of Texas at Austin, USA
University of Alberta, Canada
Air Force Institute of Technology, USA
University of Alabama, USA
Manulife Financial, Canada
Rensselaer Polytechnic Institute, USA
Pennsylvania State University, USA
Xiamen University, China
Shell, USA
Iowa State University, USA
Rensselaer Polytechnic Institute, USA
Missouri University of Science and Technology, USA
Tianjin University of Finance and Economics, China
Virginia Tech, USA
University of Delaware, USA
University of Alabama, USA
South China Normal University, China
Laboratório Nacional de Computação Cientı́fica, Brazil
Iowa State University, USA
University of California at San Diego, USA
90
Notes
91
CBC and Hyatt Place
92
9
8
3
13
To Las Vegas
Airport
ue
12
14
Student
Center
16
5
17
20
18
25
University Road
23
74
81
11
49
51
33
30
50
59
78
19
27
29
66
28
84
25
3
22
80
64
79
54
61
69
42
NUMBER
ASC
RAJ
TAC
ARC
LAC
WBS
BEH
BKS
BXG
BGC
SWC
CNC
CSB
CDC
CHE
CBC
HCH
COX
DAY
DIN
CEB-HEA
LBC
CEB
PES
TBE
EPA
FMA
22
24
Swenson Street
ABBREV.
Emergency
Phones
Interfaith
19
15
4
Academic Success Center, Claude I. Howard Building
Administration & Justice, James E. Rogers Center for
Alumni Center, Richard Tam
Architecture Building, Paul B. Sogg
Athletic Complex, Lied
Baseball Stadium, Earl E. Wilson
Beam Hall, Frank and Estella
Bookstore, UNLV
Boxing Gymnasium
Boys and Girls Club, John D. "Jackie" Gaughan
Café, SideWalk
Catholic Newman Center
Campus Services Building
Central Desert Complex
Chemistry
Classroom Building Complex, Carol C. Harter
Concert Hall, Artemus W. Ham
Cox Pavilion
Dayton Complex
Dining Commons, Hazel M. Wilson
Education Auditorium, Holbert H. Hendrix
Education Center, Lynn Bennett Early Childhood
Education, William D. Carlson
Elementary School, Paradise
Engineering Complex, Thomas T. Beam
Environmental Protection Agency
Facilities Management Administration
BUILDING NAME
11
et
10
7
Stre
sels
Brus
6
Tr
o
2
1
ca
pi
na
Av
en
Lan
e
ey
93
Joe
De
lan
To Las Vegas
Boulevard
31
30
28
29
40
41
33
Pida
Plaza
36
37
34
John S.
Wright
Hall
83
89
73
82
31
52
43
13
34
56
67
75
20
37
65
8
76
36
87
40
1
2
85
4
48
68
53
NUMBER
HFA
FND
LFG
GRA
GUA
BHS
HWB
HOU
FDH
SFB
TTL
BSL
LDS
LLB
WHI
SAM
MCB
MSM/HRC
BMC
O&M
PAR
PCT
PKG1
PKG2
MPE
BPB
BDC
72
77
74
78
64
50
81
63
57
61
60
55
79
Tam
RichardCenter
Alumni
54
Archie C. Grant
Hall
80
Harmon Avenue
65
53
Peter Johann
Soccer Field
59
82
62
56
84
86
Flashlight 85
87
88
Cottage Grove Avenue
Flamingo Road
Flamingo Access Road
PSB
PRO
RPL
RWC
RRC
RAB
TON
HUH
RHB
RHC
MFH
CWH
KRH
WBH
RHW
WRL
SEB
MSB
EMS
SSC
SU
SCS
TAY
TEC
FTC
JBT
TMC
CET
GHT
NTS
STS
UNH
USB
WRI
ABBREV.
44
38
71
5
58
41
21
18
17
15
14
6
9
7
10
16
62
55
46
24
32
70
57
72
47
86
26
77
63
60
12
45
39
35
NUMBER
http://maps.unlv.edu
Main/Paradise Campus
3D Building Map
83
58
57
Public Safety, Claude I. Howard
Publications/Reprographics/Copy Center
Radiation Protection Laboratory
Recreation and Wellness Center, Student
Recycling Center, Rebel
Research Administration Building
Residence Complex, Tonopah
Residence Hall - Building A, Mitzi & Johnny Hughes
Residence Hall - Building B, Gym Road
Residence Hall - Building C, Gym Road
Residence Hall - Building D, Margie & Robert Faiman
Residence Hall, Claudine Williams
Residence Hall, Kitty Rodman
Residence Hall, William S. Boyd
Resident Services Building, Gym Road South
Residential Life Building, Eugene R. Warner
Science and Engineering Building
Soccer Building, Robert Miller
Softball Stadium, Eller Media
Student Services Complex
Student Union
System Computing Services
Taylor Hall, William D.
Technology Building
Tennis Complex, Frank and Vicki Fertitta
Theatre, Judy Bayley
Thomas & Mack Center
Trailer, Carlson Education
Trailer, Greenhouse
Trailer Site, North
Trailer Site, South
University Hall
University Systems Building
Wright Hall, John S.
BUILDING NAME
way
Park
76
52
49
51
66
75
73
Alumni
Amphitheatre
70
71
67
d
ylan
Mar
ABBREV.
35
69
48
68
Myron Patridge
Track Stadium
Bill “Wildcat” Morris
Rebel Park
Paradise Road
44 45
47
38
32
43
42
39
Alumni
Walk
Intramural
Fields
46
Harmon Avenue
Fine Arts, Alta Ham
Foundations Building
Geoscience, Lilly Fong
Grant Hall, Archie C.
Greenspun Hall
Health Sciences, Rod Lee Bigelow
Herman Westfall Building
Houssels Building
Humanities, Flora Dungan
International Gaming Institute, Stan Fulton Building
Labs, Temporary Teaching
Law, William S. Boyd School of
LDS Institute of Religion Student Center
Library, Lied
Life Sciences, Juanita Greer White
Maintenance, Student Affairs
Moot Court, Thomas & Mack
Museum, Marjorie Barrick and Harry Reid Center
Music Center, Lee and Thomas Beam
Operations and Maintenance
Paradise Campus
Paradise Campus Trailers
Cottage Grove Parking Garage
Tropicana Parking Garage
Physical Education, Paul McDermott
Physics, Robert L. Bigelow
Professional Development Center, Bennett
BUILDING NAME
21
23
26
27
Naples Drive
UNLV Campus Map
Proceedings
All participants are invited to submit a manuscript to Proceedings of the 8th International
Conference on Scientific Computing and Applications, which will be published by the American Mathematical Society in the Contemporary Mathematics book series. A PDF version of
your original manuscript (prepared using the Contemporary Mathematics author package:
http://www.ams.org/authors/procpackages) should be submitted to [email protected]
by July 4th, 2012. The reviews of all papers will be finished by Sept.1, 2012. All contributors will get a free copy of the book from AMS. Details can be found at our conference website (http://web.unlv.edu/centers/cams/conferences/sca2012/sca2012.html) under
“Proceedings”.
Since its first classes were held on campus in 1957, UNLV has transformed itself from a small
branch college into a thriving urban research institution of more than 28,000 students and
3,100 faculty and staff.
Along the way, the urban university has become an indispensable resource in one of the
country’s fastest-growing and most enterprising cities.
The Department of Mathematical Sciences offers Ph.D degree in mathematics and statistics.
The Ph.D. program has four areas of concentration: Pure Math; Appl Math; Computational
Math and Statistics.
Contact Information
University of Nevada Las Vegas
4505 S. Maryland Pkwy
Las Vegas, NV 89154–4020
Phone: (702) 895-3567
Fax: (702) 895-4343

The conference brochure - University of Nevada, Las Vegas

Transcription

Similar documents

simulform - KnowTech3D

HPC and numerical modeling tools at the Chilean Weather

Math English D 041-050

Dear Sailing Friend: We need your help! Your support makes our

another way of using bernoulli`s method

With the Orchestre symphonique de Québec Conducted by Airat

About APSYS Models and Features Application Demonstrations

Numerical Methods

Gospel Spirituality - Christian Brothers College