ON THE GENERAL SOLUTION BY A DIRECT METHOD OF A LARGE-SCALE SINGULAR SYSTEM OF LINEAR EQUATIONS : APPLICATION TO THE ANALYSIS OF FLOATING STRUCTURES
ON THE GENERAL SOLUTION BY A DIRECT METHOD OF A LARGE-SCALE SINGULAR SYSTEM OF LINEAR EQUATIONS : APPLICATION TO THE ANALYSIS OF FLOATING STRUCTURES
复制标题
大型奇异线性方程组的直接法通解:在浮动结构分析中的应用
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
M. Géradin
中科院分区：
文献类型：
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作者：
C. Farhat;M. Géradin
Finding the general solution of a singular system of linear equations requires computing a particular solution and a basis of the null space of the corresponding singular matrix. In this paper, we consider the case where the singular matrix is large and sparse, and the application calls for a direct solution method. We highlight the dependence of straightforward factorization algorithms on an arbitrary constant that can influence the correctness of the computed solution, and describe a family of improved direct solution methods that alleviate this problem. For structural mechanics applications, we propose a hybrid geometric–algebraic method that is more robust than the purely algebraic direct methods that are currently used for solving singular sparse systems of equations. We illustrate the potential of our proposed solution algorithms with examples from structural mechanics and domain-decomposition-based iterative solvers. © 1998 John Wiley & Sons, Ltd.
