Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination
This paper proposes a parallel direct solution of flexible multibody systems based on block Gaussian elimination. The Craig–Bampton method is utilized to model flexible bodies within the multibody system, resulting in a reduction in the size of the system equations. To address the time integration p...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/15/8/4541 |
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| author | Cheng Yang Bin Xia Yuexin Wan Pin Yang Yifan Xie Zhifeng Xie |
| author_facet | Cheng Yang Bin Xia Yuexin Wan Pin Yang Yifan Xie Zhifeng Xie |
| author_sort | Cheng Yang |
| collection | DOAJ |
| description | This paper proposes a parallel direct solution of flexible multibody systems based on block Gaussian elimination. The Craig–Bampton method is utilized to model flexible bodies within the multibody system, resulting in a reduction in the size of the system equations. To address the time integration problem, an implicit stiff scheme is adopted to obtain large time step sizes. When forming the linearized systemic equations, global sparsity in the Jacobian matrix and similar local sparsity in submatrices can be observed. Subsequently, block Gaussian elimination is introduced for the direct solution of these linearized equations. The algorithm is designed to be parallelizable at the algorithm level, with a specific processing order for the submatrices of the constraints. The stability of the method is guaranteed by the positive definite and symmetric properties in the diagonal matrices in the Craig–Bampton method. The parallel efficiency and numerical stability of the method are confirmed through numerical examples in homemade codes parallelized by OpenMP. |
| format | Article |
| id | doaj-art-7b1cdd699fd14c13a75f8f8aab4a2a49 |
| institution | OA Journals |
| issn | 2076-3417 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj-art-7b1cdd699fd14c13a75f8f8aab4a2a492025-08-20T02:28:40ZengMDPI AGApplied Sciences2076-34172025-04-01158454110.3390/app15084541Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian EliminationCheng Yang0Bin Xia1Yuexin Wan2Pin Yang3Yifan Xie4Zhifeng Xie5School of Mechanical Engineering, Chengdu University, Chengdu 610106, ChinaSchool of Mechanical Engineering, Chengdu University, Chengdu 610106, ChinaSchool of Mechanical Engineering, Chengdu University, Chengdu 610106, ChinaNational Key Laboratory of Plasma Physics, Laser Fusion Research Center, Chinese Academy of Engineering Physics, Mianyang 621900, ChinaSchool of Mechanical Engineering, Chengdu University, Chengdu 610106, ChinaSchool of Aerospace Engineering, Tsinghua University, Beijing 100084, ChinaThis paper proposes a parallel direct solution of flexible multibody systems based on block Gaussian elimination. The Craig–Bampton method is utilized to model flexible bodies within the multibody system, resulting in a reduction in the size of the system equations. To address the time integration problem, an implicit stiff scheme is adopted to obtain large time step sizes. When forming the linearized systemic equations, global sparsity in the Jacobian matrix and similar local sparsity in submatrices can be observed. Subsequently, block Gaussian elimination is introduced for the direct solution of these linearized equations. The algorithm is designed to be parallelizable at the algorithm level, with a specific processing order for the submatrices of the constraints. The stability of the method is guaranteed by the positive definite and symmetric properties in the diagonal matrices in the Craig–Bampton method. The parallel efficiency and numerical stability of the method are confirmed through numerical examples in homemade codes parallelized by OpenMP.https://www.mdpi.com/2076-3417/15/8/4541flexible multibody systemCraig–Bampton methodblock Gaussian eliminationalgorithm-level paralleldirect solution |
| spellingShingle | Cheng Yang Bin Xia Yuexin Wan Pin Yang Yifan Xie Zhifeng Xie Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination Applied Sciences flexible multibody system Craig–Bampton method block Gaussian elimination algorithm-level parallel direct solution |
| title | Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination |
| title_full | Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination |
| title_fullStr | Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination |
| title_full_unstemmed | Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination |
| title_short | Parallel Direct Solution of Flexible Multibody Systems Based on Block Gaussian Elimination |
| title_sort | parallel direct solution of flexible multibody systems based on block gaussian elimination |
| topic | flexible multibody system Craig–Bampton method block Gaussian elimination algorithm-level parallel direct solution |
| url | https://www.mdpi.com/2076-3417/15/8/4541 |
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