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| Condition number and preprocessing of the finite element equation of two point boundary value problems with cubic Lagrange shape function |
| Received:May 01, 2016 |
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| DOI：10.7511/jslx201705021 |
| KeyWord:ill-conditioned seven diagonal equations special structure condition number preconditioner |
| Author | Institution |
| 张衡 |
福建师范大学福清分校 电子与信息工程学院, 福清 |
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| Abstract: |
| Solving large sparse ill-conditioned linear equations is very important in scientific computing and engineering applications.The key to solve the problem is reducing the condition number by preprocessing.The finite element system formed in solving two-point boundary value problems of integral form using the finite element method based on cubic Lagrange shape functions is converted into a system of ill-conditioned seven diagonal equations,and the condition number of the system was analyzed by studying the special structure of the equation,and the factor causing ill-conditioning was found.The big norm part of the coefficient matrix was decomposed into an assemble of several simple matrices.The preconditioner was obtained based on the decomposition,and performance analysis of the preconditioner was given in a quantitative manner.The results of analysis show that the condition number is close to 1 after pretreatment without causing more computation. |