A distributed-memory hierarchical solver for general sparse linear systems
•Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.•Proposed a new parallel algorithm for solving general sparse linear systems based on data decomposition.•Implemented a task-based asynchronous scheme by exploiting data dependency in our algorithm....
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| Veröffentlicht in: | Parallel computing Jg. 74; H. C; S. 49 - 64 |
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| Sprache: | Englisch |
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Elsevier B.V
01.05.2018
Elsevier |
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| ISSN: | 0167-8191, 1872-7336 |
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| Abstract | •Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.•Proposed a new parallel algorithm for solving general sparse linear systems based on data decomposition.•Implemented a task-based asynchronous scheme by exploiting data dependency in our algorithm.•Implemented a coloring scheme to extract concurrency in the execution.•Provided benchmarks for various problems and analysis of parallel scalability under different conditions.
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We present various numerical results to demonstrate the versatility and scalability of the parallel algorithm. |
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| AbstractList | •Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.•Proposed a new parallel algorithm for solving general sparse linear systems based on data decomposition.•Implemented a task-based asynchronous scheme by exploiting data dependency in our algorithm.•Implemented a coloring scheme to extract concurrency in the execution.•Provided benchmarks for various problems and analysis of parallel scalability under different conditions.
We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We present various numerical results to demonstrate the versatility and scalability of the parallel algorithm. We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic algorithm is faster and more memory-efficient than sparse direct solvers because it exploits the low-rank structure of fill-in blocks. Depending on the accuracy of low-rank approximations, the hierarchical solver can be used either as a direct solver or as a preconditioner. The parallel algorithm is based on data decomposition and requires only local communication for updating boundary data on every processor. Moreover, the computation-to-communication ratio of the parallel algorithm is approximately the volume-to-surface-area ratio of the subdomain owned by every processor. We also provide various numerical results to demonstrate the versatility and scalability of the parallel algorithm. |
| Author | Rajamanickam, Sivasankaran Boman, Erik G. Darve, Eric Pouransari, Hadi Chen, Chao |
| Author_xml | – sequence: 1 givenname: Chao orcidid: 0000-0002-5385-3651 surname: Chen fullname: Chen, Chao email: cchen10@stanford.edu organization: Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA – sequence: 2 givenname: Hadi surname: Pouransari fullname: Pouransari, Hadi email: hadip@stanford.edu organization: Department of Mechanical Engineering, Stanford University, Stanford, USA – sequence: 3 givenname: Sivasankaran surname: Rajamanickam fullname: Rajamanickam, Sivasankaran email: srajama@sandia.gov organization: Center for Computing Research, Sandia National Laboratories, Albuquerque, USA – sequence: 4 givenname: Erik G. surname: Boman fullname: Boman, Erik G. email: egboman@sandia.gov organization: Center for Computing Research, Sandia National Laboratories, Albuquerque, USA – sequence: 5 givenname: Eric orcidid: 0000-0002-1938-3836 surname: Darve fullname: Darve, Eric email: darve@stanford.edu organization: Institute for Computational and Mathematical Engineering, Stanford University, Stanford, USA |
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| Snippet | •Derived a new formulation of a sequential hierarchical solver, which compresses dense fill-in blocks.•Proposed a new parallel algorithm for solving general... We present a parallel hierarchical solver for general sparse linear systems on distributed-memory machines. For large-scale problems, this fully algebraic... |
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| Title | A distributed-memory hierarchical solver for general sparse linear systems |
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