gpu-accelerated design optimization on the cloud
TRANSCRIPT
GPU-Accelerated
Design Optimization
on the Cloud
Krishnan Suresh
Associate Professor
Mechanical Engineering
Design Optimization
2
Reduce weight
subject to constraints
(GE/GrabCAD)
A structure subject to loading
Design Optimization
Domains
3(OptiStruct)
(Generico)
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Big Players, Big $
� ANSYS
� Abaqus
� Altair/OptiStruct
� Nastran
� SolidWorks
� &
$10 billion investment annually technavio.com
Design Optimization on the Cloud
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Browser driven design optimization
Design Optimization on the Cloud
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Client
• No software/hardware investment
• Pay as you go
• Anywhere, anytime
• &
Service Provider
• Easier maintenance
• Larger market
• &
3D-Printing
Democratization of
fabrication
Design Optimization to 3D Printing
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Democratization of design
Catch?
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Design Optimization
DesignSpace
Finite Element Analysis(FEA)
Optimal?
ChangeDesign
No
10^5 ~ 10^7 dof
Solve Kd = f
K: Sparse SPD
100’s of iterations!
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Design Optimization Cost
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A naïve port
to cloud will not work!
� OptiStruct (commercial code)
� Xeon E5 2697, 92 GB
� 20 hours!
Cloud Based Design Optimization
Fast Limited
Memory FEA
Pareto
Optimization
GPU
Acceleration
WebGL
Fast Limited
Memory FEA
Cloud Based Design Optimization
FEA Bottleneck: Kd = f
DesignSpace
Finite Element Analysis(FEA)
Optimal?
ChangeTopology
No
10^5 ~ 10^7 dof
Solve Kd = f
K: Sparse SPD
100’s of iterations!
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==
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Kd = f (GTC)
� Fine-grained Parallel Preconditioners
� CULA
� MAGMA
� Accelerating Iterative Linear Solvers
� Efficient AMG on Hybrid GPU Clusters
� Preconditioning for Large-Scale Linear Solvers
� &
� Exploit mesh congruency
� Exploit physics behavior
� K constantly changing
� &
Design Optimization
Kd = f
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Exploit Mesh Congruency (GTC 2014)
Kd f=
Model DiscretizeAssemble/
Solve
Post-process
Mesh-aware SpMV Acceleration: Congruence
Element Congruency
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62350 elements
2780 distinct
95.5% congruent
Observation: Large-meshes contain many similar elements!
Elements are ‘rigid-body/scaling’ congruent
⇒ Identical element stiffness Ke
Only store Ke of distinct elements
Implication: SpMV
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( )1
Classic: N
e
i
Kd K d=
≡ ∑
: Sparse Matrix-Vector Multiplication (SpMV)
Critical operation in ALL iterative solvers
Kd
( )1
Assembly-free: N
e e
i
Kd K d=
≡∑
Only store Ke of distinct elements + Assembly Free
Experiment
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106 Elements
1 Distinct element
0
200
400
600
800
1000
Assembled AF-CPU AF-GPU
SpMV; Kd (msec)
770
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- Same number of FLOPS!
- Reduced memory
CPU
Mesh-aware Kd
Naïve Kd
One Kd (SpMV)
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Physics Aware Deflation
Kd f=
Model DiscretizeAssemble/
Solve
Post-process
Physics Aware Deflation
0
TK W KW=%
0K K<<%
Agglomeration/Grouping
Treat each group as rigid body
Deflated CG
Kd f=
Example
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3.15 million DOF
Fast Limited
Memory FEA
Pareto
Optimization
1. Mesh Congruency
2. AF Deflation
Cloud Based Design Optimization
Design Optimization
K Matrix: Constantly changing
� Update K?
� Update deflation?
( )1
Assembly-free: N
e e
i
Kd K d=
≡∑Skip deleted finite elements
SpMV accelerates further
0
TK W KW=%
0 ( )T
eK K W K W= − ∆% %
K K<<%
Example: Design Optimization
� OptiStruct (commercial)
� Xeon E5 2697, 92 GB
� 20 hours!
� Pareto
� I7 4770, 8 GB
� 42 mins
Framework
Fast Limited
Memory FEA
GPU
Acceleration
Pareto
Optimization
Mesh Aware SpMV on GPU
Deflation on GPU
TW dWµProlongation Restriction
Example: Design Optimization
� OptiStruct (commercial)
� Xeon E5 2697,92 GB
� 20 hours!
� Pareto
� I7 4770,8 GB
� 42 mins
� Pareto
� GTX 480,1.5 GB
� 6 mins
Cloud Based Design Optimization
Fast Limited
Memory FEA
Pareto
Optimization
GPU
Acceleration
WebGL
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WebGL & Three.js
WebGL
� JavaScript API for 3D graphics in browsers
� www.khronos.org
� Almost all browsers
ThreeJs
� Higher-level library
� www.threejs.org
� Almost all browsers
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Finally …
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A Pilot Service
www.cloudtopopt.com
� Entry level server
• E3-1270 V3
• 8 GB
� Limited to 150,000 degrees of freedom
� 300+ users
www.cloudtopopt.com
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www.cloudtopopt.com
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Plans
� Port to HPC provider
� NSF funding
� Launch startup
www.cloudtopopt.com
Acknowledgements
Praveen Yadav Shiguang Deng Amir M. Mirzendehdel Chaman Singh Alireza Taheri Bian Xiang
Anirudh Krishnakumar Anirban Niyogi Victor Cavalcanti Cameron Gilanshah Yibo Hu Alex Buehler
Funding� NSF
� Air-force
� Luvata
� Autodesk
� Sandia National Lab
[email protected] www.cloudtopopt.com