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
Hlavní autoři: Celebi, M. Serdar, Duran, Ahmet, Oztoprak, Figen, Tuncel, Mehmet, Akaydin, Bora
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2017
Springer Nature B.V
Témata:
Application programming interface
Compilers
Computer memory
Computer networks
Computer Science
Computer simulation
Distributed memory
Distributed processing
Finite element method
Interpreters
Linear equations
Mathematical analysis
Microprocessors
Mumps
Performance enhancement
Processor Architectures
Processors
Programming Languages
Public domain
Robustness (mathematics)
Solvers
State of the art
Utilities
SuperLU
Symbolic factorization
Scalability
Sparse direct solver
Reservoir simulations
Many-core distributed solver
Parallel linear direct solver
Large scale simulations
Linear equations
Numerical factorization
ISSN:0920-8542, 1573-0484
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Shrnutí: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.
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ISSN:0920-8542
1573-0484
DOI:10.1007/s11227-016-1892-7