Fully parallel and pipelined sparse direct solver for large symmetric indefinite finite element problems
Sparse linear system solving is a primary computational cost in large-scale finite element analysis, and improving its performance is a key technological challenge in this field. Real-world engineering problems involve diverse materials, elements, and connectivity relationships, making it difficult...
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| Veröffentlicht in: | Computers & mathematics with applications (1987) Jg. 175; S. 447 - 469 |
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| ISSN: | 0898-1221 |
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| Abstract | Sparse linear system solving is a primary computational cost in large-scale finite element analysis, and improving its performance is a key technological challenge in this field. Real-world engineering problems involve diverse materials, elements, and connectivity relationships, making it difficult for iterative methods to handle their global stiffness matrices. Direct methods, owing to their robustness, emerge as the preferred choice. In this paper, a novel block-based supernodal LDLT numerical factorization method is introduced. The computational process is disassembled into distinct tasks, and the dependency relationships between these tasks are expressed via a directed acyclic graph to guide the calculation sequence. Based on this approach, a global task pool and local task stack are established to store task queues, enhancing data reuse and multicore collaboration efficiency. Additionally, an effective task dispatch and work-stealing mechanism is implemented to prevent performance degradation caused by load imbalances. Numerical experiments, including a publicly available matrix test set and real-world engineering finite element problems, are conducted to compare the parallel performances of the Pardiso, MUMPS, and proposed solver. The results illustrate that the proposed solver performs significantly better than the other solvers when handling various types of sparse matrices and diverse architectures of multicore processors. |
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| AbstractList | Sparse linear system solving is a primary computational cost in large-scale finite element analysis, and improving its performance is a key technological challenge in this field. Real-world engineering problems involve diverse materials, elements, and connectivity relationships, making it difficult for iterative methods to handle their global stiffness matrices. Direct methods, owing to their robustness, emerge as the preferred choice. In this paper, a novel block-based supernodal LDLT numerical factorization method is introduced. The computational process is disassembled into distinct tasks, and the dependency relationships between these tasks are expressed via a directed acyclic graph to guide the calculation sequence. Based on this approach, a global task pool and local task stack are established to store task queues, enhancing data reuse and multicore collaboration efficiency. Additionally, an effective task dispatch and work-stealing mechanism is implemented to prevent performance degradation caused by load imbalances. Numerical experiments, including a publicly available matrix test set and real-world engineering finite element problems, are conducted to compare the parallel performances of the Pardiso, MUMPS, and proposed solver. The results illustrate that the proposed solver performs significantly better than the other solvers when handling various types of sparse matrices and diverse architectures of multicore processors. |
| Author | Wang, Shengquan Wang, Guidong Wang, Yujie Cai, Yong Li, Guangyao |
| Author_xml | – sequence: 1 givenname: Yujie surname: Wang fullname: Wang, Yujie organization: State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, Hunan University, Changsha, 410082, China – sequence: 2 givenname: Shengquan surname: Wang fullname: Wang, Shengquan organization: State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, Hunan University, Changsha, 410082, China – sequence: 3 givenname: Yong surname: Cai fullname: Cai, Yong email: caiyong@hnu.edu.cn organization: State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, Hunan University, Changsha, 410082, China – sequence: 4 givenname: Guidong surname: Wang fullname: Wang, Guidong organization: State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, Hunan University, Changsha, 410082, China – sequence: 5 givenname: Guangyao surname: Li fullname: Li, Guangyao organization: Shenzhen Automotive Research Institute, Beijing Institute of Technology, Shenzhen 518118, Guangdong, China |
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| Cites_doi | 10.1016/j.advengsoft.2022.103290 10.1016/j.cpc.2021.108190 10.1016/j.camwa.2021.04.013 10.1016/j.parco.2021.102870 10.1002/nme.1620090207 10.1109/SUPERC.1990.129995 10.1145/1326548.1326550 10.1016/j.jcp.2015.10.012 10.1016/j.enganabound.2023.09.004 10.1137/090757216 10.1016/S0167-739X(00)00076-5 10.1137/18M1225963 10.1002/cnm.2607 10.1016/j.parco.2014.02.003 10.1016/S0168-9274(01)00115-5 10.1016/j.cageo.2021.104901 10.1137/0611010 10.1145/567806.567807 10.1016/j.finel.2010.11.005 10.1137/110846427 10.1016/j.cpc.2022.108637 10.1145/2629641 10.1016/j.simpat.2013.09.004 10.1002/cpe.4460 10.1137/04061043X 10.1016/j.jcp.2013.10.017 10.1111/1365-2478.12132 10.1137/0610013 10.1016/j.acme.2013.05.009 10.1016/j.jpdc.2009.09.007 10.1002/cnm.887 10.1002/1098-2760(20000820)26:4<265::AID-MOP18>3.0.CO;2-O 10.1016/j.cpc.2017.12.006 10.1016/j.parco.2016.06.004 10.1137/S0895479897317685 10.1002/nla.2183 |
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