MPS Sim - Related Publications

1
MPS Sim - Related Publications
[And96]
B. D. O. Anderson. New developments in the theory of positive systems. In C.I. Byrnes, editor,
Systems and Control in the Twenty-First Century, volume 22 of Progr. Systems Control Theory,
pages 17–36. Birkhäuser, Boston, MA, 1997.
[AndCNST00] A.R.A. Anderson, M.A.J. Chaplain, E.L. Newmann, R.J.C. Steele, and A.M. Thompson. Mathematical modelling of tumour invasion and metastasis. J. Theor. Med., 2:129–154, 2000.
[Arn98]
M. Arnold. Zur Theorie und zur numerischen Lösung von Anfangswertproblemen für differentiellalgebraische Systeme von höherem Index. Fortschritt-Berichte VDI Reihe 20, Nr. 264. VDI–Verlag,
Düsseldorf, 1998.
[ArnS00]
M. Arnold and B. Simeon. Pantograph and catenary dynamics: A benchmark problem and its
numerical solution. Appl. Numer. Math., 34(4):345–362, 2000.
[AscP95]
U.M. Ascher and L.R. Petzold. The numerical solution of delay-differential-algebraic equations of
retarded and neutral type. SIAM Journal on Scientific and Statistic Computing, 32(5):1635–1657,
1995.
[Bac03]
A. Backes. Optimale Steuerung der linearen DAE im Fall Index 2. Preprint 2003-04, Institut für
Mathematik, Humboldt-Universität zu Berlin, 2003.
[Bac06]
A. Backes. Extremalbedingungen für Optimierungs-Probleme mit Algebro-Differentialgleichungen.
PhD thesis, Institut für Mathematik, Humboldt-Universität zu Berlin, 2006.
[Bae07]
S. Bächle. Numerical Solution of Differential-Algebraic Systems Arising in Circuit Simulation. PhD
thesis, Institute of Mathematics, Technische Universität Berlin, 2007.
[BaeE05a] S. Bächle and F. Ebert. Graph theoretical algorithms for index reduction in circuit simulation.
Technical Report 245, M ATHEON - DFG Research Center ”Mathematics for key techonolgies”,
2005.
[BakPT02] C. T. H. Baker, C. A. H. Paul, and H. Tian. Differential algebraic equations with after-effect. J.
Comput. Appl. Math., 140(1-2):63–80, March 2002.
[BalKM06] K. Balla, G.A. Kurina, and R. März. Index criteria for differential algebraic equations arising from
linear-quadratic optimal control problems. J. Dyn. Control Syst., 12(3):289–311, 2006.
[BalL05]
K. Balla and V.H. Linh. Adjoint pairs of differential-algebraic equations and Hamiltonian systems.
Appl. Numer. Math., 53(2-4):131–148, 2005.
[BalM02]
K. Balla and R. März. A unified approach to linear differential algebraic equations and their adjoints.
Z. Anal. Anwendungen, 21(3):783–802, 2002.
[BarBS11] A. Bartel, S. Baumanns, and S. Schöps. Structural analysis of electrical circuits including magnetoquasistatic devices. Applied Numerical Mathematics, 61(12):1257–1270, 2011.
[BelZ03]
A. Bellen and M. Zennaro. Numerical Methods for Delay Differential Equations. Clarendon Press,
2003.
[BenF02]
L. Benvenuti and L. Farina. Positive and compartmental systems. IEEE Trans. Automat. Control,
47:370–373, 2002.
[BenSF03] L. Benvenuti, A. De Santis, and L. Farina, editors. Positive systems, volume 294 of Lecture Notes
in Control and Information Sciences. Springer, Berlin, 2003.
[BirV58]
G. Birkhoff and R. S. Varga. Reactor criticality and non-negative matrices. J. Soc. Indust. Appl.
Math., 6:354–377, 1958.
[BlaK04]
W. Blajer and K. Kołodziejczyk. A geometric approach to solving problems of control constraints:
theory and a DAE framework. Multibody Syst. Dyn., 11(4):343–364, 2004.
[BreCP96] K.E. Brenan, S.L. Campbell, and L.R. Petzold. Numerical Solution of Initial-Value Problems in Differential Algebraic Equations, volume 14 of Classics in Applied Mathematics. SIAM, Philadelphia,
PA, 1996.
[BreF91]
F. Brezzi and M. Fortin. Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York,
1991.
[Cam80]
S.L. Campbell. Singular linear systems of differential equations with delays. Applicable Analysis,
2:129–136, 1980.
2
[Cam83]
S.L. Campbell. One canonical form for higher index linear time varying singular systems. Circuits,
Systems and Signal Processing, 2:311–326, 1983.
[Cam91]
S.L. Campbell. Comments on 2-d descriptor systems. Automatica, 27(1):189–192, 1991.
[Cam95a]
S. L. Campbell. High index differential algebraic equations. 23:199–222, 1995.
[Cam95c]
S. L. Campbell. Nonregular 2D descriptor delay systems. IMA J. Math. Control Appl., 12:57–67,
1995.
[CamG95] S.L. Campbell and C.W. Gear. The index of general nonlinear DAEs. Numerische Mathematik,
72(2):173–196, 1995.
[CamL09]
S.L. Campbell and V.H. Linh. Stability criteria for differential-algebraic equations with multiple
delays and their numerical solutions. Applied Mathematics and Computation, 208(2):397–415,
2009.
[Cap93]
V. Capasso. Mathematical Structures of Epidemic Systems. Springer Verlag, Berlin, 1993.
[ComM06] C. Commault and N. Marchand, editors. Positive systems, volume 341 of Lecture Notes in Control
and Information Sciences, Berlin, 2006. Springer Verlag.
[CroR73]
M. Crouzeix and P.-A. Raviart. Conforming and nonconforming finite element methods for solving
the stationary Stokes equations. I. Rev. Franc. Automat. Inform. Rech Operat, 7(R-3):33–75, 1973.
[DFG10]
A. Jahnke. Antrag zum Honigmann-Prozess an die Deutsche Forschungsgemeinschaft, 2010.
[EicF98]
E. Eich-Soellner and C. Führer.
Stuttgart, 1998.
[Ern09]
T. Erneux. Applied Delay Differential Equations. Springer, 2009.
[ErnV13]
A. Ern and M. Vohralı́k. Adaptive inexact Newton methods with a posteriori stopping criteria for
nonlinear diffusion PDEs. SIAM J. Sci. Comput., ??:??–??, 2013.
[EstT00]
D. Estévez Schwarz and C. Tischendorf. Structural analysis of electric circuits and consequences
for MNA. International Journal of Circuit Theory and Applications, 28(2):131–162, 2000.
[FarR00]
L. Farina and S. Rinaldi. Positive Linear Systems: Theory and its Applications. John Wiley and
Sons Inc., New York, 2000.
[Fri04]
P. Fritzson. Principles of Object-Oriented Modeling and Simulation with Modelica 2.1. Wiley-IEEE
Computer Society Pr, Linköping, 2004.
Numerical Methods in Multibody Dynamics.
B.G.Teubner,
[FriALNPSB05] P. Fritzson, P. Aronsson, H. Lundvall, K. Nystrm, A. Pop, L. Saldamli, and D. Broman. The
openmodelica modeling, simulation, and development environment, 2005.
[Fue88]
C. Führer. Differential-algebraische Gleichungssysteme in mechanischen Mehrkörpersystemen Theorie, numerische Ansätze und Anwendungen. PhD thesis, Technische Universität München,
1988.
[Gan97]
G. Gandolfo. Economic Dynamics. Springer Verlag, Heidelberg, 1997.
[Gea88]
C.W. Gear. Differential-algebraic equation index transformations. SIAM Journal on Scientific and
Statistic Computing, 9:39–47, 1988.
[Gea90]
C.W. Gear. Differential algebraic equations, indices, and integral algebraic equations. SIAM Journal on Numerical Analysis, 27(6):1527–1534, 1990.
[GeaLG85] C.W. Gear, B. Leimkuhler, and G.K. Gupta. Automatic integration of Euler-Lagrange equations
with constraints. Journal of Computional and Applied Mathematics, 12/13:77–90, 1985.
[GeaP84]
C.W. Gear and L.R. Petzold. ODE methods for the solution of differential/algebraic systems. SIAM
Journal on Numerical Analysis, 21:716–728, 1984.
[Ger03]
M. Gerdts. Optimal control and real-time optimization of mechanical multi-body systems. Z. Angew.
Math. Mech., 83(10):705–719, 2003. ECMI-Workshop “Numerical Methods in Multibody Dynamics” (Bad Herrenalb, 2001).
[Ger06]
M. Gerdts. Local minimum principle for optimal control problems subject to differential-algebraic
equations of index two. J. Optim. Theory Appl., 130(3):443–462, 2006.
[GirR86]
V. Girault and P.-A. Raviart. Finite Element Methods for Navier-Stokes Equations. Springer-Verlag,
Berlin, 1986.
3
[Glu02]
H. Gluesing-Luerssen. Linear Delay-Differential Systems with Commensurate Delays : An Algebraic Approach. Springer, 2002.
[GreS00]
P. M. Gresho and R. L. Sani. Incompressible flow and the finite element method. Vol. 2: Isothermal
laminar flow. Wiley, Chichester, UK, 2000.
[Gri92]
E. Griepentrog. Index reduction methods for differential-algebraic equations. In E. Griepentrog,
M. Hanke, and R. März, editors, Seminar Notes - Berliner Seminar on Differential-Algebraic Equations (Seminarbericht 92-1), Humboldt Universität zu Berlin, 1992.
[GriM86]
E. Griepentrog and R. März. Differential-Algebraic Equations and Their Numerical Treatment,
volume 88 of Teubner-Texte zur Mathematik. BSB B.G.Teubner Verlagsgesellschaft, Leipzig, 1986.
[GueF99a] M. Günther and U. Feldmann. CAD-based electric-circuit modeling in industry, I. Mathematical
structure and index of network equations. Surveys on Mathematics for Industry, 8:97–129, 1999.
[GueF99b] M. Günther and U. Feldmann. CAD-based electric-circuit modeling in industry, II. Impact of circuit
configuration and parameters. Surveys on Mathematics for Industry, 8:131–157, 1999.
[HaM12ppt] P. Ha and V. Mehrmann. Analysis and reformulation of linear delay differential-algebraic equations.
Preprint 08–2012, Institut für Mathematik, Technische Universität Berlin, 2012. Aug. 1, 2012,
accepted for publication in Electronic Journal on Linear Algebra.
[HaiLR89] E. Hairer, C. Lubich, and M. Roche. The Numerical Solution of Differential-Algebraic Systems by
Runge-Kutta Methods. Springer-Verlag, Berlin, Germany, 1989.
[HaiW96]
E. Hairer and G. Wanner. Solving Ordinary Differential Equations II - Stiff and Differential-Algebraic
Problems. Springer-Verlag, Berlin, Germany, 2nd edition, 1996.
[HaiWWW] E. Hairer. website http://www.unige.ch/∼hairer/software.html.
[HalL93]
J.K. Hale and S.M.V. Lunel. Introduction to Functional Differential Equations. Springer, 1993.
[Ham03]
P. Hamann. Modellierung und Simulation von realen Planetengetrieben. Diploma thesis, Institut
für Mathematik, Technische Universität Berlin, Berlin, Germany, 2003. in cooperation with DaimlerChrysler AG.
[Hei11]
G. Heiderich.
Einfluss strukturviskosen Verhaltens von Kunststoffschmelzen bei
Drehzahländerungen auf Druckverhältnisse im Schneckenvorraum des extruders. Bachelor
thesis, Fachbereich Maschinenbau, Universität Paderborn, Paderborn, Germany, 2011.
[Hon85]
M. Honigmann. Storing power, December 1885. US Patent 333,222.
[Hon86]
M. Honigmann. Storing power, April 1886. US Patent 340,718.
[HunKLV94] W. Hundsdorfer, B. Koren, M. van Loon, and J.G. Verwer. A positive finite-difference advection
scheme. J. Comp. Phys., 117:35–46, 1994.
[HunV03]
W. Hundsdorfer and J. G. Verwer. Numerical Solution of Time-Dependent Advection-DiffusionReaction Equations. Springer Verlag, Berlin, 2003.
[IVPtestset] J. Kierzenka, C. Magharini, and F. Mazzia.
http://www.dm.uniba.it/∼testset).
[Jah92]
Test set for IVP solvers, Release 2.4. (website
M. Jahnich. Numerische lösungen differential-algebraischer gleichungssysteme zur simulation
verkoppelter temperatur- und strömungsprozesse in der kunststoffextrusionstechnik. Diploma thesis, Fachbereich Elektrotechnik, Universität Gesamthochschule Paderborn, Paderborn, Germany,
1992.
[JahFJSWZ13] A. Jahnke, C. Fleßner, T. Jungnickel, L. Strenge, N. Wolf, and F. Ziegler. First cycle simulations
of the honigmann process with libr/h2o and naoh/h2o as working fluid pairs as a thermochemical
energy storage. International Journal of Low-Carbon Technologies, 8(suppl 1):i55–i61, 2013.
[JahPD93] M. Jahnke, K. Popp, and B. Dirr. Approximate analysis of flexible parts in multibody systems using
the finite element method. In W. Schiehlen, editor, Advanced Multibody System Dynamics, pages
237–256. Kluwer Academic Publishers, Stuttgart, 1993.
[Kac02]
T. Kaczorek. Positive 1D and 2D Systems. Springer Verlag, London, 2002.
[Kin11]
J. King, K. Unterkofler, G. Teschl, S. Teschl, and A. Amann. Breath gas analysis for estimating
physiological processes using anesthetic monitoring as a prototypic example. In Engineering in
Medicine and Biology Society, EMBC, 2011 Annual International Conference of the IEEE, pages
1001–1004. IEEE, 2011.
4
[KinEtAl11] J. King, K. Unterkofler, G. Teschl, S. Teschl, H. Koc, H. Hinterhuber, and A. Amann. A mathematical
model for breath gas analysis of volatile organic compounds with special emphasis on acetone. J.
Math. Biol., 63(5):959–999, 2011.
[KurM04]
G.A. Kurina and R. März. On linear-quadratic optimal control problems for time-varying descriptor
systems. SIAM J. Control Optim., 42(6):2062–2077, 2004.
[KurM07]
G.A. Kurina and R. März. Feedback solutions of optimal control problems with DAE constraints.
SIAM J. Control Optim., 46(4):1277–1298, 2007.
[Lue79]
D. G. Luenberger. Introduction to Dynamic Systems. John Wiley and Sons Inc., New York, NY,
1979.
[M01]
R. März. Adjoint equations of differential-algebraic systems and optimal control problems. Proceedings of Belarussian National Academy of Sciences, Institute of Mathematics, 7:88–97, 2001.
[MatS93]
S. Mattsson and G. Söderlind. Index reduction in differential-algebraic equations using dummy
derivatives. SIAM Journal on Scientific and Statistic Computing, 14:677–692, 1993.
[MehPV96] V. Mehrmann, T. Penzl, and A. Varga. A new slicot implementation and documentation standard.
WGS Newsletter 10, 1996. Available under http://www.win.tue.nl/niconet/NIC2/reports.html.
[NedP05]
N.S. Nedialkov and J.D. Pryce. Solving differential-algebraic equations by Taylor series (i): Computing Taylor coefficients. BIT Numerical Mathematics, 45(3):561–591, 2005.
[NedP07]
N.S. Nedialkov and J.D. Pryce. Solving differential-algebraic equations by Taylor series (ii): Computing the system Jacobian. BIT Numerical Mathematics, 47(1):121–135, 2007.
[NedP08]
N.S. Nedialkov and J.D. Pryce. Solving differential-algebraic equations by Taylor series (III): The
DAETS code. Journal of Numerical Analysis, Industrial and Applied Mathematics, 3:61–80, 2008.
[NedPT12] N.S. Nedialkov, J. Pryce, and G. Tan. DAESA - a Matlab tool for structural analysis of DAEs:
Software. Technical report CAS-12-01-NN, Department of Computing and Software, McMaster
University, Hamilton, ON, Canada, July 2012.
[Pan88]
C.C. Pantelides. The consistent initialization of differential-algebraic systems. SIAM Journal on
Scientific and Statistic Computing, 9:213–231, 1988.
[Pet82]
L.R. Petzold. Differential/algebraic equations are not ODEs. SIAM Journal on Scientific and Statistic Computing, 3:367–384, 1982.
[Pet86]
L.R. Petzold. Order results for implicit Runge-Kutta methods applied to differential/algebraic systems. SIAM Journal on Numerical Analysis, pages 837–852, 1986.
[PinV97]
M.d.R. de Pinho and R.B. Vinter. Necessary conditions for optimal control problems involving
nonlinear differential algebraic equations. J. Math. Anal. Appl., 212(2):493–516, 1997.
[PolW97]
J.W. Polderman and J.C. Willems. Introduction to mathematical systems theory. A behavioral
approach. Springer, New York, 1997.
[Pry01]
J. Pryce. A simple structural analysis method for DAEs. BIT Numerical Mathematics, 41:364–394,
2001.
Keyword: Mathematics and Statistics
[QuaNPS93] A.R. Quarles, T.and Newton, D.O. Pederson, and A. Sangiovanni-Vincentelli. Spice 3 user manual. Technical report, Department of Electrical Engineering and Computer Sciences, University of
California, 1993.
[ReiMB00] G. Reißig, W. S. Martinson, and P. I. Barton. Differential-algebraic equations of index 1 may have
an arbitrarily high structural index. SIAM Journal on Scientific Computing, 21:1987–1990, 2000.
[ReiS10b] T. Reis and T. Stykel. PABTEC: Passivity-preserving balanced truncation for electrical circuits.
IEEE Trans. Computer-Aided Design Integr. Circuits Syst., 29(9):1354–1367, 2010.
[RheS99]
W. C. Rheinboldt and B. Simeon. Computing smooth solutions of DAEs for elastic multibody
systems. Comput. Math. Appl., 37(6):69–83, 1999.
[Ria08]
R. Riaza. Differential-Algebraic Systems: Analytical Aspects and Circuit Applications. World Scientific Publishing Company, Incorporated, 2008.
[Rod86]
L. Rodman, I. Gohberg, and P. Lancaster. Invariant Subspaces of Matrices with Applications. John
Wiley and Sons Inc., New York, NY, 1986.
5
[Rot30]
E. Rothe. Zweidimensionale parabolische Randwertaufgaben als Grenzfall eindimensionaler
Randwertaufgaben. Math. Ann., 102(1):650–670, 1930.
[Ruz04]
M. Ružička. Nichtlineare Funktionalanalysis: Eine Einführung. Springer-Verlag, London, 2004.
[SchZ07]
J. Schöberl and W. Zulehner. Symmetric indefinite preconditioners for saddle point problems with
applications to PDE-constrained optimization problems. SIAM J. Matrix Anal. Appl., 29(3):752–773
(electronic), 2007.
[ShaG06]
L. F. Shampine and P. Gahinet. Delay-differential-algebraic equations in control theory. Appl.
Numer. Math., 56(3-4):574–588, March 2006.
[She95]
J. Shen. On error estimates of the penalty method for unsteady Navier-Stokes equations. SIAM J.
Numer. Anal., 32(2):386–403, 1995.
[Sim06]
B. Simeon. On Lagrange multipliers in flexible multibody dynamics. Comput. Method. Appl. M.,
195(50–51):6993–7005, 2006.
[Sim13]
B. Simeon. Computational flexible multibody dynamics. A differential-algebraic approach.
Differential-Algebraic Equations Forum. Springer-Verlag, Berlin, 2013.
[Sim98a]
B. Simeon. Order reduction of stiff solvers at elastic multibody systems. Appl. Numer. Math.,
28(2–4):459–475, 1998.
[SimFR91] B. Simeon, C. Führer, and P. Rentrop. Diffrential-algebraic equations in vehicle system dynamics.
Surveys on Mathematics for Industry, 1:1–37, 1991.
[Smi10]
H.L. Smith. An Introduction to Delay Differential Equations with Applications to the Life Sciences.
Springer, 2010.
[Son98]
E.D. Sontag. Mathematical control theory. Deterministic finite dimensional systems. 2nd ed.
Springer, New York, 1998.
[StoW08]
M. Stoll and A. Wathen. Combination preconditioning and the Bramble-Pasciak+ preconditioner.
SIAM J. Matrix Anal. Appl., 30(2):582–608, 2008.
[TayH73]
C. Taylor and P. Hood. A numerical solution of the Navier-Stokes equations using the finite element
technique. Internat. J. Comput. & Fluids, 1(1):73–100, 1973.
[Tem91]
R. Temam. Remark on the pressure boundary condition for the projection method. Theor. Comp.
Fluid. Dyn., 3:181–184, 1991.
[Ver96]
R. Verfürth. A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques.
Wiley-Teubner, Stuttgart, 1996.
[Vir08]
E. Virnik. Stability analysis of positive descriptor systems. Linear Algebra Appl., 429:2640–2659,
2008.
[VlaS94]
J. Vlach and K. Singhal. Computer Methods for Circuit Analysis and Design. Van Nostrand Reinhold, New York, 1994.
[VohW13]
M. Vohralı́k and M. F. Wheeler. A posteriori error estimates, stopping criteria, and adaptivity for
two-phase flows. Comput. Geosci., 2013.
[monk]
P. Monk. Finite Element Methods for Maxwell’s Equations, Numerical Mathematics and Scientific
Computation. Oxford University Press, New York, 2003.
[purcell1963electricity] E. M. Purcell. Electricity and Magnetism, volume 2. Tata McGraw-Hill Education, 1963.