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Transcript of 1 Parallel Simulations of Underground Flow in Porous and Fractured Media H. Mustapha 1,2, A....
1
Parallel Simulations Parallel Simulations of Underground Flow of Underground Flow
in Porous and Fractured in Porous and Fractured MediaMedia
H. MustaphaH. Mustapha1,21,2, A. Beaudoin, A. Beaudoin11, J. Erhel, J. Erhel11 and J.R. and J.R. De DreuzyDe Dreuzy22
1 - IRISA – INRIA de Rennes1 - IRISA – INRIA de Rennes
2 - Géosciences de Rennes2 - Géosciences de Rennes
2
OutlineOutline
Problem presentation Problem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solver Parallel linear solver Direct solver - PSPASESDirect solver - PSPASES Iterative solver – HYPRE Iterative solver – HYPRE
Results and performancesResults and performances Tests and architectureTests and architecture Complexity and scalability analysis with PSPASESComplexity and scalability analysis with PSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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OutlineOutline
Problem presentationProblem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solver Parallel linear solver Direct solver - PSPASESDirect solver - PSPASES Iterative solver – HYPRE Iterative solver – HYPRE
Results and performancesResults and performances Tests and architectureTests and architecture Complexity and scalability analysis with PSPASESComplexity and scalability analysis with PSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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GeometricalGeometrical model model
Discrete fracture network Discrete fracture network
3D fracture network3D fracture network2D porous media2D porous media
Heterogeneous hydraulic Heterogeneous hydraulic conductivity fieldconductivity field
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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EquationsEquations
Q = - K*Q = - K*grad (hgrad (h) )
div (Q) = 0div (Q) = 0 BoundaryBoundary conditions conditions
Flow fluid modelFlow fluid model
Fixed head
Nul flux
3D fracture network3D fracture network
Fix
ed
head
Fix
ed
head
Nul flux
Nul flux
2D porous media2D porous media
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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OutlineOutline
Problem presentationProblem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix Numerical method and parallel matrix
generationgeneration
Parallel linear solver Parallel linear solver direct solver – PSPASES direct solver – PSPASES iterative solver – HYPRE iterative solver – HYPRE
Result and performancesResult and performances tests and architecturetests and architecture complexity and scalability analysis with PSPASEScomplexity and scalability analysis with PSPASES comparison between PSPASES and HYPREcomparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Conforming Conforming triangular triangular
meshmesh
Regular gridRegular grid
Assembled by all corresponding sub-domains linear systemsAssembled by all corresponding sub-domains linear systems
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
Mixed Hybrid Finite Element MethodMixed Hybrid Finite Element Method
Type of meshType of mesh
Global linear systemGlobal linear system
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OutlineOutline
Problem presentationProblem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solverParallel linear solver Direct solver – PSPASES Direct solver – PSPASES Iterative solver – HYPRE Iterative solver – HYPRE
Results and performancesResults and performances Tests and architectureTests and architecture Complexity and scalability analysis with PSPASESComplexity and scalability analysis with PSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
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Parallel Linear solverParallel Linear solver Direct solver – PSPASESDirect solver – PSPASES
sparse matricessparse matrices
symmetric positive definite matricessymmetric positive definite matrices
distributed-memory paradigm and MPI librarydistributed-memory paradigm and MPI library
P (number of processors) = 2^NP (number of processors) = 2^N
Cholesky factorizationCholesky factorization
Iterative solver – HYPREIterative solver – HYPRE
sparse matricessparse matrices
V-cycle multi-grid algorithm (SMG)V-cycle multi-grid algorithm (SMG)
distributed-memory paradigm and MPI librarydistributed-memory paradigm and MPI library
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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OutlineOutline
Problem presentationProblem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solver Parallel linear solver Direct solver – PSPASES Direct solver – PSPASES Iterative solver - HYPREIterative solver - HYPRE
Results and performancesResults and performances Parallel architectureParallel architecture Complexity and scalability analysis with PSPASESComplexity and scalability analysis with PSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
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Parallel architectureParallel architecturedistributed memorydistributed memory
2 nodes of 32 bi – processors 2 nodes of 32 bi – processors (Proc AMD Opteron 2Ghz with 2Go (Proc AMD Opteron 2Ghz with 2Go
of RAM)of RAM)
Parallel architectureParallel architecture
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
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OutlineOutline
Problem presentation Problem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solver Parallel linear solver Direct solver – PSPASES Direct solver – PSPASES Iterative solver - HYPREIterative solver - HYPRE
Results and performancesResults and performances Parallel architectureParallel architecture Complexity and scalability analysis with Complexity and scalability analysis with
PSPASESPSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
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Test 1Test 1 : CPU time of matrix generation, linear solving and flow : CPU time of matrix generation, linear solving and flow computation obtained with two processorscomputation obtained with two processors
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
Complexity analysis with PSPASESComplexity analysis with PSPASES
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Test 2 :Test 2 : Memory requirements for both applications Memory requirements for both applications
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
Complexity analysis with PSPASESComplexity analysis with PSPASES
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Scalability analysis with PSPASESScalability analysis with PSPASES
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
PTp
TE S
PTp
NR
P N Tp R
2 2,6 105 5.60 1.20 106
8 1,05 106 11.33 1.18 106
32 4,19 106 25.70 1,04 106
4 2,6 105 2.92 1.15 106
16 1,05 106 6.06 1.11 106
64 4,19 106 13.08 1,05 106
P N Tp R
2 2,6 105 13.10 10006
8 1,05 106 22.06 5942
32 4,19 106 38.41 341
4 2,6 105 7.94 16508
16 1,05 106 16.05 4083
64 4,19 106 No value No value
2D medium 3D fracture network
Test 1 :Test 1 : Efficiency Efficiency
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Scalability analysis with PSPASESScalability analysis with PSPASES
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
TpT2S 2 Test 2 :Test 2 : Speed-up Speed-up
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OutlineOutline
Problem presentationProblem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solver Parallel linear solver Direct solver - PSPASESDirect solver - PSPASES Iterative solver - HYPREIterative solver - HYPRE
Results and performancesResults and performances Parallel architectureParallel architecture Complexity and scalability analysis with PSPASESComplexity and scalability analysis with PSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
18
Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Test 1 :Test 1 : Linear solving time Linear solving time
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
PSPASESHYPRE
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Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Test 2 :Test 2 : Speed-up Speed-up
HYPRE PSPASES
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
20
OutlineOutline
Problem presentationProblem presentation Geometrical and flow fluid modelGeometrical and flow fluid model Numerical method and parallel matrix generationNumerical method and parallel matrix generation
Parallel linear solver Parallel linear solver Direct solver – PSPASES Direct solver – PSPASES Iterative solver – HYPRE Iterative solver – HYPRE
Results and performancesResults and performances Parallel architectureParallel architecture Complexity and scalability analysis with PSPASESComplexity and scalability analysis with PSPASES Comparison between PSPASES and HYPREComparison between PSPASES and HYPRE
Conclusions and future workConclusions and future work
H. Mustapha INRIA, Parco sept 2005
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
21
ConclusionsConclusions
Future workFuture work
Parallel Simulations of Underground Flow in Porous Parallel Simulations of Underground Flow in Porous and Fractured Mediaand Fractured Media
H. Mustapha INRIA, Parco sept 2005
Direct solver PSPASES
Iterative solver HYPRE
Scalable in the case of 2D medium
Not scalable in the case of 3D fracture network
• A 3D extension of parallel software in the case of 2D porous media
• Parallel software for simulating solute migration
Efficient for large linear systems