On the improvement of a scalable sparse direct solver for unsymmetrical linear equations
This paper focuses on the application level improvements in a sparse direct solver specifically used for large-scale unsymmetrical linear equations resulting from unstructured mesh discretization of coupled elliptic/hyperbolic PDEs. Existing sparse direct solvers are designed for distributed server...
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| Vydáno v: | The Journal of supercomputing Ročník 73; číslo 5; s. 1852 - 1904 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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01.05.2017
Springer Nature B.V |
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| ISSN: | 0920-8542, 1573-0484 |
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| Abstract | This paper focuses on the application level improvements in a sparse direct solver specifically used for large-scale unsymmetrical linear equations resulting from unstructured mesh discretization of coupled elliptic/hyperbolic PDEs. Existing sparse direct solvers are designed for distributed server systems taking advantage of both distributed memory and processing units. We conducted extensive numerical experiments with three state-of-the-art direct linear solvers that can work on distributed-memory parallel architectures; namely, MUMPS (MUMPS solver website,
http://graal.ens-lyon.fr/MUMPS
), WSMP (Technical Report TR RC-21886, IBM, Watson Research Center, Yorktown Heights,
2000
), and SUPERLU_DIST (ACM Trans Math Softw 29(2):110–140,
2003
). The performance of these solvers was analyzed in detail, using advanced analysis tools such as Tuning and Analysis Utilities (TAU) and Performance Application Programming Interface (PAPI). The performance is evaluated with respect to robustness, speed, scalability, and efficiency in CPU and memory usage. We have determined application level issues that we believe they can improve the performance of a distributed-shared memory hybrid variant of this solver, which is proposed as an alternative solver [SuperLU_MCDT (Many-Core Distributed)] in this paper. The new solver utilizing the MPI/OpenMP hybrid programming is specifically tuned to handle large unsymmetrical systems arising in reservoir simulations so that higher performance and better scalability can be achieved for a large distributed computing system with many nodes of multicore processors. Two main tasks are accomplished during this study: (i) comparisons of public domain solver algorithms; existing state-of-the-art direct sparse linear system solvers are investigated and their performance and weaknesses based on test cases are analyzed, (ii) improvement of direct sparse solver algorithm (SuperLU_MCDT) for many-core distributed systems is achieved. We provided results of numerical tests that were run on up to 16,384 cores, and used many sets of test matrices for reservoir simulations with unstructured meshes. The numerical results showed that SuperLU_MCDT can outperform SuperLU_DIST 3.3 in terms of both speed and robustness. |
|---|---|
| AbstractList | This paper focuses on the application level improvements in a sparse direct solver specifically used for large-scale unsymmetrical linear equations resulting from unstructured mesh discretization of coupled elliptic/hyperbolic PDEs. Existing sparse direct solvers are designed for distributed server systems taking advantage of both distributed memory and processing units. We conducted extensive numerical experiments with three state-of-the-art direct linear solvers that can work on distributed-memory parallel architectures; namely, MUMPS (MUMPS solver website,
http://graal.ens-lyon.fr/MUMPS
), WSMP (Technical Report TR RC-21886, IBM, Watson Research Center, Yorktown Heights,
2000
), and SUPERLU_DIST (ACM Trans Math Softw 29(2):110–140,
2003
). The performance of these solvers was analyzed in detail, using advanced analysis tools such as Tuning and Analysis Utilities (TAU) and Performance Application Programming Interface (PAPI). The performance is evaluated with respect to robustness, speed, scalability, and efficiency in CPU and memory usage. We have determined application level issues that we believe they can improve the performance of a distributed-shared memory hybrid variant of this solver, which is proposed as an alternative solver [SuperLU_MCDT (Many-Core Distributed)] in this paper. The new solver utilizing the MPI/OpenMP hybrid programming is specifically tuned to handle large unsymmetrical systems arising in reservoir simulations so that higher performance and better scalability can be achieved for a large distributed computing system with many nodes of multicore processors. Two main tasks are accomplished during this study: (i) comparisons of public domain solver algorithms; existing state-of-the-art direct sparse linear system solvers are investigated and their performance and weaknesses based on test cases are analyzed, (ii) improvement of direct sparse solver algorithm (SuperLU_MCDT) for many-core distributed systems is achieved. We provided results of numerical tests that were run on up to 16,384 cores, and used many sets of test matrices for reservoir simulations with unstructured meshes. The numerical results showed that SuperLU_MCDT can outperform SuperLU_DIST 3.3 in terms of both speed and robustness. This paper focuses on the application level improvements in a sparse direct solver specifically used for large-scale unsymmetrical linear equations resulting from unstructured mesh discretization of coupled elliptic/hyperbolic PDEs. Existing sparse direct solvers are designed for distributed server systems taking advantage of both distributed memory and processing units. We conducted extensive numerical experiments with three state-of-the-art direct linear solvers that can work on distributed-memory parallel architectures; namely, MUMPS (MUMPS solver website, http://graal.ens-lyon.fr/MUMPS ), WSMP (Technical Report TR RC-21886, IBM, Watson Research Center, Yorktown Heights, 2000), and SUPERLU_DIST (ACM Trans Math Softw 29(2):110–140, 2003). The performance of these solvers was analyzed in detail, using advanced analysis tools such as Tuning and Analysis Utilities (TAU) and Performance Application Programming Interface (PAPI). The performance is evaluated with respect to robustness, speed, scalability, and efficiency in CPU and memory usage. We have determined application level issues that we believe they can improve the performance of a distributed-shared memory hybrid variant of this solver, which is proposed as an alternative solver [SuperLU_MCDT (Many-Core Distributed)] in this paper. The new solver utilizing the MPI/OpenMP hybrid programming is specifically tuned to handle large unsymmetrical systems arising in reservoir simulations so that higher performance and better scalability can be achieved for a large distributed computing system with many nodes of multicore processors. Two main tasks are accomplished during this study: (i) comparisons of public domain solver algorithms; existing state-of-the-art direct sparse linear system solvers are investigated and their performance and weaknesses based on test cases are analyzed, (ii) improvement of direct sparse solver algorithm (SuperLU_MCDT) for many-core distributed systems is achieved. We provided results of numerical tests that were run on up to 16,384 cores, and used many sets of test matrices for reservoir simulations with unstructured meshes. The numerical results showed that SuperLU_MCDT can outperform SuperLU_DIST 3.3 in terms of both speed and robustness. |
| Author | Celebi, M. Serdar Duran, Ahmet Akaydin, Bora Tuncel, Mehmet Oztoprak, Figen |
| Author_xml | – sequence: 1 givenname: M. Serdar surname: Celebi fullname: Celebi, M. Serdar email: mscelebi@itu.edu.tr organization: Informatics Institute, Istanbul Technical University – sequence: 2 givenname: Ahmet surname: Duran fullname: Duran, Ahmet organization: Department of Mathematics, Istanbul Technical University – sequence: 3 givenname: Figen surname: Oztoprak fullname: Oztoprak, Figen organization: Department of Industrial Engineering, Bilgi University – sequence: 4 givenname: Mehmet surname: Tuncel fullname: Tuncel, Mehmet organization: Informatics Institute, Istanbul Technical University, Department of Mathematics, Istanbul Technical University – sequence: 5 givenname: Bora surname: Akaydin fullname: Akaydin, Bora organization: Informatics Institute, Istanbul Technical University |
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| Cites_doi | 10.1145/1089014.1089017 10.1007/s11227-014-1344-1 10.1023/A:1019119117297 10.1145/779359.779361 10.1007/BF00130109 10.1016/S0045-7825(99)00242-X 10.1137/S0895479897317685 10.1137/S0895479899358194 10.1137/1.9780898718881 10.1109/71.598277 10.1137/S0895479894278952 10.1137/S0895479895291765 10.1007/978-3-319-09873-9_41 10.1142/9789812797766_0003 10.1137/050638102 |
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| Keywords | SuperLU Symbolic factorization Scalability Sparse direct solver Reservoir simulations Many-core distributed solver Parallel linear direct solver Large scale simulations Linear equations Numerical factorization |
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| References | Arabnia, Taha (CR23) 1998; 10 Gupta, Karypis, Kumar (CR1) 1997; 8 CR19 Arabnia, Bhandarkar (CR22) 1996; 10 Demmel, Eisenstat, Gilbert, Li, Liu (CR9) 1999; 20 CR16 Demmel, Gilbert, Li (CR3) 1999; 20 CR15 CR14 CR13 CR12 Xiaoye (CR17) 2005; 31 Davis Timothy (CR7) 2006 Li, Demmel (CR6) 2003; 29 Amestoy, Duff, LExcellent (CR5) 2000; 184 Steward (CR18) 1973 CR8 Duran, Celebi, Piskin, Tuncel (CR24) 2015; 71 Amestoy, Duff, Koster, LExcellent (CR4) 2001; 23 CR28 CR27 CR26 CR25 CR21 CR20 Amestoy, Davis, Duff (CR11) 1996; 17 Demmel, Gilbert, Xiaoye (CR10) 1999; 20 Gupta, Koric, George (CR2) 2009 A Davis Timothy (1892_CR7) 2006 1892_CR20 PR Amestoy (1892_CR5) 2000; 184 1892_CR21 JW Demmel (1892_CR3) 1999; 20 HR Arabnia (1892_CR23) 1998; 10 1892_CR8 SL Xiaoye (1892_CR17) 2005; 31 JW Demmel (1892_CR9) 1999; 20 HR Arabnia (1892_CR22) 1996; 10 1892_CR26 1892_CR27 A Gupta (1892_CR2) 2009 1892_CR25 1892_CR28 PR Amestoy (1892_CR11) 1996; 17 GW Steward (1892_CR18) 1973 PR Amestoy (1892_CR4) 2001; 23 JW Demmel (1892_CR10) 1999; 20 A Gupta (1892_CR1) 1997; 8 1892_CR12 A Duran (1892_CR24) 2015; 71 1892_CR15 1892_CR16 1892_CR13 1892_CR14 1892_CR19 XS Li (1892_CR6) 2003; 29 |
| References_xml | – volume: 31 start-page: 302 issue: 3 year: 2005 end-page: 325 ident: CR17 article-title: An overview of SuperLU: algorithms, implementation, and user interface publication-title: ACM Trans Math Softw doi: 10.1145/1089014.1089017 – volume: 71 start-page: 938 issue: 3 year: 2015 end-page: 951 ident: CR24 article-title: Scalibility of OpenFOAM for bio-medical flow simulations publication-title: J Supercomput doi: 10.1007/s11227-014-1344-1 – ident: CR14 – ident: CR16 – year: 2009 ident: CR2 publication-title: SC09 Proceedings – ident: CR12 – volume: 10 start-page: 185 issue: 1–2 year: 1998 end-page: 202 ident: CR23 article-title: A parallel numerical algorithm on a reconfigurable multi-ring network publication-title: Telecommun Syst doi: 10.1023/A:1019119117297 – volume: 29 start-page: 110 issue: 2 year: 2003 end-page: 140 ident: CR6 article-title: SuperLU_DIST: a scalable distributed-memory sparse direct solver for unsymmetric linear systems publication-title: ACM 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| Title | On the improvement of a scalable sparse direct solver for unsymmetrical linear equations |
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