Parallel Wave Propagation and Topological Operators for Fragmentation Simulation
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Parallel Wave Propagation and Topological Operators for Fragmentation Simulation
Glaucio H. Paulino
Professor, Faculty CEE, MechSE, CSE
Donald Biggar Willett Professor of Engineering
6th Annual Workshop on CHARM++ and its Applications
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4/15/2008 2http//cee.uiuc.edu/paulino [email protected]
Acknowledgments
CEE COLLABORATOR:
Mr. Kyoungsoo Park
CS COLLABORATORS:
Prof. Laxmikant V. Kale (UIUC)
Dr. Celso L. Mendes (UIUC)
Dr. Terry L. Wilmarth (UIUC)
Mr. Aaron Becker (UIUC)
Mr. Isaac Dooley (UIUC)
Prof. Waldemar Celes (PUC-Rio)
Mr. Rodrigo Espinha (PUC-Rio)
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Stress waves
Waves
Rosakis AJ, Samudrala O, Coker D, 1999, Science 284
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Outline
Waves Wave Propagation
Rayleigh wave Parallel computing: ParFUM Results: Geological simulation
Dynamic Fracture Cohesive zone modeling Node Perturbation & Edge-Swap Operation Results: Fracture & Compact compression tests
Summary Future Work
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Wave Propagation: Rayleigh Wave
Surface Wave
Lord Rayleigh, 1885
Seismology, Geology, Material Science, etc
Homogeneous & Orthotropic materials (2005)
Large-Scale 3D Analysis for Graded media
• Rayleigh L. 1885, On waves propagated along the plane surface of an elastic solid, Proc. R. Soc. Lond. A 17, 4-11
• Vinh PC, Ogden RW. 2005, On the Rayleigh wave speed in orthotropic elastic solids, Meccanica 40, 147-161.
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Parallel Computing: ParFUM
Finite Element Analysis
Bill Gropp: Very “Easy to write code that
scales and performs poorly.”
Time Integration
Central difference method
Communications
Update Rint
Shared-node summation operation
21
12n n n nt tu u u u+ = +D + D& &&
1 int1 1 1( )ext
n n n-
+ + += -u M R R&&
1 1( )2n n n n
t+ +
D= + +u u u u& & && &&
Lawler OS, Chakravorty S, Wilmarth TL, Choudhury N, Dooley I, Zheng G, Kale LV, 2006, ParFUM: a parallel framework for unstructured meshes for scalable dynamic physics applications, Engineering with Computers 22, 215-235.
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Machine Specification
Dell Cluster [Abe] Peak FLOPS: 89.47 TF Number of Blades (nodes): 1200 Number of CPUs (cores): 9600 Processor: Intel 64 2.33GHz dual socket quad core 8 MB L2 cache (2 MB) Memory: 8GB (1GB) Total: 9600 GB
Dell Xeon Cluster [Tungsten] Peak FLOPS: 16.38 TF Number of nodes: 1280 Number of processors: 2560 Processor: Intel Xeon 3.2 GHz (32-bit) Memory: 1.5 GB Total: 3840 GB
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0
2000
4000
6000
8000
10000
32 64 128 256 512 1024
Runtime Performance
Number of processors
Par
alle
l ru
nti
me
(sec
) # of Elements: 0.4 million
91%
90%
81%62% 43%
Dell Cluster [Abe]
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Geology Simulation: Rayleigh Wave
Layer #4
Layer #3
Layer #2
Layer #1 (Graded)
4km
2km
2km
2km
10 km
10 km
Layer #4
Homogeneous
10km
10 km
10 km
z
P(t) P(t)
( ) sin(2 ) (0 2)
( ) 0 ( 2)
P t t t
P t t
p= £ £
= >
V. Pereyra, E. Richardson, S. E. Zarantonello, Large scale calculations of 3D elastic wave propagation in a complex geology, Proceedings of the 1992 ACM/IEEE conference on Supercomputing, Minneapolis, Minnesota, 301-309.
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Homogeneous Media
Material Properties
Dynamic Responses
CP (km/s)
CS (km/s)
ρ(kg/m3)
E (MPa) v
Media 2 1.2 2 7.02 0.219
Tim
e (sec)
5
4
3
2
1
( ) 1/f r r
1
1.01
CR = 1.1 km/s
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Graded & Layered Media
( ) 1/f r r
( ) 1/f r r
CP (km/s)
CS (km/s)
p(kg/m3)
E (MPa) v
Graded Layer #1
23.6
1.22.16
23.6
7.0240.94
0.2190.219
Layer #2 3.5 2.1 2.3 24.7 0.336
Layer #3 4.5 2.1 2.3 27.6 0.361
Layer #4 5.5 2.1 2.3 28.7 0.430
Tim
e (sec)
5
4
3
2
1
1
1.25
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Waves Wave Propagation
Rayleigh wave Parallel computing: ParFUM Results: Geology simulation
Dynamic Fracture Cohesive zone modeling Node Perturbation & Edge-Swap Operation Results: Fracture & Compact compression tests
Summary Future Work
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Dynamic Fracture: Cohesive Zone
Cohesive Zone Model
Computational Simulation TRULY Extrinsic cohesive surface elements
Several claims of extrinsic simulations in the literature are NOT truly extrinsic (e.g. activated elements are not extrinsic)
Ce-basedTi-basedXi XK et al., 2005,, Physical Review Letters, 94, 125510
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Topology-based Data Structure
Complete Topological Data
Reduced Representation
Support for Adaptive Analysis
• W. Celes, G.H. Paulino, R. Espinha, 2005, Efficient handling of implicit entities in reduced mesh representations, Journal of Computing and Information Science in Engineering 5 (4), 348-359.
• W. Celes, G.H. Paulino, R. Espinha, 2005, A compact adjacency-based topological data structure for finite element mesh representation, IJNME 64(11), 1529-1556
• G. H. Paulino, W. Celes, R. Espinha, Z. Zhang, 2008, A general topology-based framework for adaptive insertion of cohesive elements in finite element meshes, EWC 24, 59-78
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Entity Enumeration
Model
Entity information
Elapsed time (s)
Topologicalentity
Number of entities
Titan IV model (linear hexahedral
mesh)
Element 1,738,240 0.097
Node 1,845,640 0.046
Facet 5,321,600 0.219
Edge 5,429,000 0.292
Vertex 1,845,640 0.186
W. Celes, G.H. Paulino, R. Espinha, 2005, Efficient handling of implicit entities in reduced mesh representations, Journal of Computing and Information Science in Engineering 5 (4), 348-359.
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4K Structured Mesh
Mesh Orientation Dependence 4 direction Maximum error: 45º
8 direction Maximum error: 22.5º
Undesirable crack pattern
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Node Perturbation
Edge Swap
Proposed Remediation
0.0 0.1 0.3
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Crack Length Convergence
Simulation Outline Find the shortest path
(e.g. ) Node Perturbation (NP) Factor: 0.3 Edge Swap Square 4K structured mesh Element size: 0.1 Simulate 100 randomly perturbed
meshes for each node perturbation factor
1
2.4
1tan (2.4) 67.38
2.6ExactL
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Results
NP 0.3
Avg. Error = 5.5%
NP 0.3 & Edge Swap
Avg. Error = 4.5%NP0, Error = 8.2%
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Crack Angle Convergence
67.38
NP Factor = 0 NP Factor (0.3) & Edge swap
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Effect of Element Size & Edge-SwapA
ng
le (
º)
Element Size
Activate Edge Swap (ES)
Without Edge Swap (ES)
NP Factor = 0.3Given Angle (α)
0 10 20 30 40 50
50.2
53.1
56.3
59.7
63.4
67.4
71.6
76.0
An
gle
(º)
The number of appearance
Element Size = 0.1
45
50
55
60
65
70
75
80
0 0.05 0.1 0.15 0.2
with edge-swap
without edge-swap
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Fracture Test (Verification)
0 0.0124
16 mm
4.2 mm
4K structured mesh (80 X 21)
Material PropertiesE = 3.24 GPav = 0.35ρ = 1190 kg/m3
GI = 352 N/mσmax = 129.6 MPa
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[mm]
Compact Compression Specimen
Incident bar Transmitter bar
60
70
2035
16
E = 5.76 GPav = 0.42ρ = 1182 kg/mm3
GI = GII = 4800 N/mσmax = 105 MPa
striker
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Summary
Large-Scale Parallel Wave Propagation 1024 processors
Rayleigh Wave Speed in 3D Functionally Graded Media
Crack Path Representation thru Topological representation Node perturbation & Edge swap operators
Adaptive Dynamic Fracture Simulation V & V
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Future Work
Wave propagation for complex geology systems Provide guidance to estimate Rayleigh wave speed in
smoothly graded heterogeneous media
Incorporate data from geological surveys
Parallel Dynamic Fracture Simulation Parallel adaptive insertion of cohesive surface element
Dynamic adaptive load balancing
There is a lot of exciting work to do !