CSC Format Global Matrix Storage Algorithm Considering Constraints

Zheng-fang DONG , Jia-hao WANG , Yun-hua LI , Wei CHENG , Jun-jie WANG

Science Technology and Engineering ›› 2025, Vol. 25 ›› Issue (10) : 4265 -4273.

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Science Technology and Engineering ›› 2025, Vol. 25 ›› Issue (10) : 4265-4273 DOI: 10.12404/j.issn.1671-1815.2403703
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CSC Format Global Matrix Storage Algorithm Considering Constraints
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Abstract

In order to improve the efficiency of finite element analysis and reduce memory consumption, the storage algorithm of the overall matrix was studied. The constraints were uniformly processed as matrix partitions at the element level. Subsequently, taking the stiffness matrix as an example, the distribution pattern of non-zero elements under the constrained condition was determined. A calculation method and corresponding formulas suitable for the number of non-zero elements in the stiffness matrix of two-dimensional and three-dimensional finite elements were proposed, and the correctness was verified. The correspondence between one-dimensional equal bandwidth storage and the original square matrix address was deduced, and it was applied as an auxiliary array in the process of integrating the overall matrix in CSC format, which has improved the efficiency of the overall matrix assembly and avoided the difficulty of node numbering optimization. Finally, the correctness and practicability of the proposed algorithm were verified by using thefourspan single-line girder bridge in the Changdao section of the Fangshan Line in Beijing. The results show that the overall matrix assembly time is reduced by 30%, the storage space is saved by more than 68%, and the calculation efficiency of linear equations is improved by more than 71% while ensuring the calculation accuracy.

Keywords

finite element method / stiffness matrix / non-zero elements / compressed storage / cholesky decomposition

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Zheng-fang DONG, Jia-hao WANG, Yun-hua LI, Wei CHENG, Jun-jie WANG. CSC Format Global Matrix Storage Algorithm Considering Constraints. Science Technology and Engineering, 2025, 25(10): 4265-4273 DOI:10.12404/j.issn.1671-1815.2403703

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