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G-Pre: A Graph-Theory-Based Matrix Preconditioning Algorithm for Finite Element Simulation Solutions
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Kang Liang,
Gai Wu ,
Wei Shen
Applied Sciences, Volume: 15, Issue: 9, Start page: 5130
Swansea University Author:
Lijie Li
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DOI (Published version): 10.3390/app15095130
Abstract
In finite element simulation and analysis, increasing simulation scales place high demands on the preconditioning and solution process of linear matrices. However, the most commonly used preconditioning methods for incomplete LU factorization usually increase data access and computation due to data...
| Published in: | Applied Sciences |
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| ISSN: | 2076-3417 |
| Published: |
MDPI AG
2025
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| Online Access: |
Check full text
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa69671 |
| Abstract: |
In finite element simulation and analysis, increasing simulation scales place high demands on the preconditioning and solution process of linear matrices. However, the most commonly used preconditioning methods for incomplete LU factorization usually increase data access and computation due to data padding and forward/backward operations, as well as affect parallel computing design. To address these challenges, this study proposes a graph–theory-based matrix preconditioning algorithm called G-Pre. In this method, by introducing a graph partitioning algorithm and a graph rearrangement algorithm before ILU factorization, the matrix is partitioned into regions and the elements are rearranged, which improves the ease of data access for matrix computation and facilitates parallel computation. The results of numerical experiments show that in terms of solution efficiency, the solver based on the G-Pre preconditioning algorithm achieved an average speedup ratio of 2.1 and 4.3 times that of the solver based on ILU factorization and the direct solver, respectively. At the same time, the algorithm computed the results with an error of no more than 2%. This method is a novel technique for the matrix preconditioning of finite element solvers and a powerful algorithmic tool to cope with the increasing computational demands of finite element simulations. |
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| Keywords: |
graph reordering; factorization; preconditioning; matrix solving; finite element simulation |
| College: |
Faculty of Science and Engineering |
| Funders: |
This work was financially supported by the National Key Research and Development Program of China (No. 2024YFF0504903), the Knowledge Innovation Program of Wuhan-Shuguang (Grant Nos. 2023010201020255 and 2023010201020243), the Natural Science Foundation of Wuhan (Grant No. 2024040801020222), the National Natural Science Foundation of China (Grant Nos. 52202045 and 92473102), the Shenzhen Science and Technology Program (Grant No. JCYJ20240813175906008), the China Scholarship Council (Grant No. 202206275005), and the State Key Laboratory of Intelligent Vehicle Safety Technology. |
| Issue: |
9 |
| Start Page: |
5130 |