1988 Fiscal Year Final Research Report Summary
Development of Solver for A Large Sparse Set of Linear Algebraic Equations for Supercomputer - Modified Conjugate Gradient Method
| Project/Area Number |
62550339
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
土木構造
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| Research Institution | OKAYAMA UNIVERSITY |
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Principal Investigator |
TANIGUCHI Takeo Associate Professor, Okayama University, 工学部, 助教授 (30026322)
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| Project Period (FY) |
1987 – 1988
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| Keywords | Modified Conjugate Gradient Method / Linear Algebraic Equations / Preconditioner / Incomplete Choleski Factorization / プレコンディショナー |
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| Research Abstract |
This investigation is for the development of a new solver for a large sparse set of linear algebraic equations which engineers encounter at the application of Finite Element Method to their field. In order to utilize the supercomputer effectively, the solver to be introduced should be one of terative ones, and the modified conjugate gradient method is selected for this purpose. This solver consists of two parts; the preconditioner and the conjugate gradient method. In order to improve the convergence behaviour of the solver the former must be carefully selected. At present incomplete choleski factorization is most effective for sparse matrices in structural analysis, and it is introduced for this study. Through a number of numerical experiments, they clarified that in many cases the solver failed in the computations, and at present there exists no effective preconditioner which can lead to good solutions. In this investigation new preconditioner is proposed by modifing the preconditioner which is proposed by Ajiz ＆ Jennings. By introducing this preconditioner to the conjugate gradient method any kind of sparse matrices can be solved, and the behaviour of the convergence by the new solver is as same as the one by the robust method. This suggests new solver is effective and useful as a general-purpose solver for a large sparse set of linear algebraic equations.
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