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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Main Authors: Cheng Yang, Bin Xia, Yuexin Wan, Pin Yang, Yifan Xie, Zhifeng Xie
Format: Article
Language:English
Published: MDPI AG 2025-04-01
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.
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institution OA Journals
issn 2076-3417
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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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AT pinyang paralleldirectsolutionofflexiblemultibodysystemsbasedonblockgaussianelimination
AT yifanxie paralleldirectsolutionofflexiblemultibodysystemsbasedonblockgaussianelimination
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