| Project/Area Number |
09680327
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
計算機科学
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| Research Institution | The University of Tokyo |
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Principal Investigator |
OYANAGI Yoshio The University of Tokyo, School of Science, Professor, 大学院・理学系研究科, 教授 (60011673)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIDA Akira The University of Tokyo, School of Science, 大学院・理学系研究科, 助手 (60302808)
SUDA Reiji Nagoya University, School of Engineering, 大学院・工学研究科, 講師 (40251392)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥3,000,000 (Direct Cost: ¥3,000,000)
Fiscal Year 1998: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 1997: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | linear equation / unstructured grid / CG method / preconditioning / parallelization / domain decomposition / multi-grid / block Jacobi / 偏微分方程式 / 離散化 / 並列処理 / 共役勾配法 / ICCG法 / Jocobi法 / 多重積分 / 有限要素法 / 領域分割法 |
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| Research Abstract |
In this research, the solution of linear equations which come out from the discretization of partial differenctial equations by an unstructured grid is studied with special emphasis on parallel processing.
1) Preconditoning of the Bi-CGSTAB method
We proposed a Multi-Grid preconditioning of the Bi-CGSTAB method and applied this MGBI-CGSTAB method to a convection-diffusion equation discretized on an unstructured grid. We showed that this algorithm gives better convergence behavior than the MILU preconditioning and is applicable to wide area of problems of this type.
2) Domain Decomposiotion Method based on interior point elimination
We proposed a new domain decomposition method where the boundary consists of double array of points. Although this scheme requires twice larger number of boudary points, the structure of the resulting capacitance matrix becomes simple so that the preconditioning based on diagonal block can be applied parallelly. We also implemented a parallelization where one domain is handled by multiple PU's.
3) Precoditioning method for general positive symmetric matrix
A general preconditoning method for an irregular matrix which comes from the discretization on an unstructured grid. Since the ICCG method is hard to parallelize, we proposed a variant of block Jacobi preconditioning and implemented it on a parallel machine. This pre-conditioning is easily parallelizable and gives better convergence properties than the point Jacobi. preconditioning.
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