Ideal case: extension-inflation test

Simulating Human Aorta Material Behavior
Using a GPU Explicit Finite Element Solver
Vukasin Strbac†, David M. Pierce‡, Jos Vander Sloten†, Nele Famaey†
†Biomechanics Section, Mechanical Engineering,
KULeuven, Leuven, BE
‡Mechanical Engineering, Biomedical Engineering,
Mathematics, Interdisciplinary Mechanics Lab
University of Connecticut, Storrs, CT, US
Vukasin Strbac
GTC2016
Introduction: general biomech. motivation
 Accelerating FE analysis provides new clinical opportunities:



pre-operative (e.g. faster custom stent design)
intra-operative stress monitoring
post-operative damage monitoring/fatigue estimation at lower cost
 Ever-advancing capabilities of modern hardware, e.g. GPGPUs, offer
opportunities to accelerate established algorithms
heterogeneous composition, aorta
Vukasin Strbac
tissue behavior
GTC2016
angioplasty
stenting
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2/21
Introduction: core facts
 Explicit FE is pleasingly parallel (for the most part)
 Explicit FE is sensitive to material and geometric parameters
 Complex material model is necessary for accurate results
 GPUs are sensitive to floating point precision used
 What can we expect?


How does anisotropy affect GPU explicit FE?
How do hexahedral element formulations affect GPU explicit FE?
Particularly in terms of Gaussian integration schemes

How does that affect our research?
Vukasin Strbac
GTC2016
14.04.16
3/21
Introduction: GPU-based FE solver
 𝑴 {𝒖} + 𝑐𝑑 [𝑴]{𝒖} + {𝑭 𝒖 } = [𝑹]
 Nonlinear, explicit, large strain, central differences
Assign Boundary
Conditions
 Trilinear hexahedral elements, unstructured grid
 Templated

single/double precision, textures, output, etc..
per
element
 Boundary conditions: kinematic, constant force, pressure
 Materials – following slides (linear, nonlinear)
 Pre-processing

Custom input file structure for geometry, material and BCs
 Post-processing


 Validated against
Abaqus (Dassault Systèmes) and
-
FEAP(University of California, Berkeley)
Assemble global
internal force
vector
Forward timemarching step
Check energy
balance
Binary .vtu files + Paraview
Real-time rendering
-
per
node
Compute stress
Integrate stress
n
Co
nv?
y
End
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GTC2016
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4/21
Element technology: Biofidelic materials
•
H
Compute stress
Integrate stress
Linear elastic model (Hookean)
𝜎𝑖𝑗 = 𝑓 𝜖𝑖𝑗 = λ𝛿𝑖𝑗 𝜖𝑖𝑗 + 2𝜇𝜖𝑖𝑗 = Cε
•
Nonlinear elastic model, isotropic (neo-Hookean)
𝜕Ψ
)
𝜕𝑭
𝜎 = 𝑓(
NH
•
Nonlinear elastic, anisotropic (fiber-reinforced arterial tissue model [Gasser et al., 2006])
GHO
Anisotropic constituent
[Weisbecker et al., 2012]
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Element technology: Gaussian integration
ζ
UI
ξ
µ
ζ
FI
ξ
Under-integration
-Fast
-Inaccurate
-Hourglassing
-No volumetric locking
-No shear locking
Compute stress
Integrate stress
Arithmetic
expense
Memory
expense
1x
1x
(Not appropriate for anisotropic materials
with low mesh density)
Full integration (FI)
-Slow
-Very accurate
-Volumetric locking
-Shear locking
~8x
~3x
Selective reduced (SR)
-Very slow
-Very accurate
-No volumetric locking
-Shear locking
~9x
~4x
µ
ζ
SR
ξ
µ
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GTC2016
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Ideal case: extension-inflation test

Extension 5% + systolic pressure

Reference solutions

FEAP & ABAQUS

We implement the same materials in all solvers

We solve using 3 different generations: Fermi,
Kepler and Maxwell (no optimization)

GHO material (+neo-Hooke for ref.)

Scaling

Convergence criteria based on
reference solutions


RMS < 0.0005mm
deltaRMS < 0.0001mm
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Ideal case: extension-inflation test
Under-integration
Full integration
Selective-reduced integration
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Ideal case: extension-inflation test
FERMI
(C2075)
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Ideal case: extension-inflation test
KEPLER
(K20c)
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GTC2016
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Ideal case: extension-inflation test
MAXWELL
(GTX980)
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GTC2016
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Ideal case: extension-inflation test
Anisotropy cost
(GHO/NH)
Integration cost
(SR/UI)
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GTC2016
14.04.16
12/21
Ideal case: conclusions
 Speed-ups are considerable
 Difficult to say exactly why one GPU is faster in a specific scenario
 No architecture-specific considerations are employed, speedup is free
 Useful for



Parameter-fitting and geometry identification
Sensitivity analyses
…anything made possible by large numbers of FE simulations
 Not a clinically accurate scenario
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GTC2016
14.04.16
13/21
Near incompressibility and floating point precision
MPa
Single
precision
Double
precision
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GTC2016
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FI
UI
SR
Double
Single
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GTC2016
14.04.16
15/21
Clinically relevant test case: AAA inflation
p1
p2
p3
p4
p5
Patient-specific FE meshes of abdominal aortic aneurysms [Tarjuelo-Gutierrez et al., 2014]
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GTC2016
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16/21
Clinically relevant test case: AAA inflation
thrombus
 The ‘silent killer’
 Peak Wall Stress (PWS) estimate needed
 Thrombus:


Separation
Different material
 Layer specific material properties
aorta
Vukasin Strbac
GTC2016
14.04.16
17/21
Presenter
Type of presentation
14.04.16
18/21
Clinically relevant test case: AAA inflation
p1
p2
p3
p4
p5
FEAP[h]
21.12
22.79
21.01
21.52
21.86
CUDA[h]
2.93
1.22
2.75
3.03
1.31
factor
x7.2
x18.7
x7.6
x7.1
x16.8
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GTC2016
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Poisson = 0.4995
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GTC2016
14.04.16
20/21
Conclusion
 We maintain significant speedup even using state-of-the-art materials, highorder integration and double precision on GPUs, with no compromise
whatsoever on accuracy. Even for less than ideal meshes.
 Single precision becomes ineffective quickly, and depends on Poisson ratio.
Double precision is necessary.
 Practical opportunities, enabling technology:



FE sensitivity analysis
Inverse FE simulations
Indications of clinical use
 Generally:



Memory-bound algorithm
Lots of random reads and atomic writes due to unstructured grid
For details on implementation/optimization see: S4497, Strbac GTC2014
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GTC2016
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21/21
Thank you for your attention.
Questions?
Vukasin Strbac
GTC2016
14.04.16
22/21