1999 Fiscal Year Final Research Report Summary
Mathematical Study of the Boundary Element Method and its Application to Inverse
| Project/Area Number |
10490018
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
広領域
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| Research Institution | KYOTO UNIVERSITY |
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Principal Investigator |
ISO Yuusuke Kyoto Univ., Graduate School of Informatics, Professor, 情報学研究科, 教授 (70203065)
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| Co-Investigator(Kenkyū-buntansha) |
NISHIMURA Naoshi Kyoto Univ., Graduate School of Engnieering, Associate Professor, 工学研究科, 助教授 (90127118)
若野 功 京都大学, 情報学研究科, 助手 (00263509)
KUBO Masayoshi Kyoto Univ., Graduate School of Informatics, Lecturer, 情報学研究科, 講師 (10273616)
木村 正人 広島大学, 理学研究科, 講師 (70263358)
ONISHI Kazuei Ibaraki Univ., Fuculty of Science, Professor, 理学部, 教授 (20078554)
NISHIDA Takaaki Kyoto Univ., Gaduate School of Science, Professor (70026110)
TANAK Masataka Shinshu Univ., Fuculty of Engineering, Professor (40029319)
KUBO Shiro Osaka Univ., Graduate School of Engnieering, Professor (20107139)
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| Project Period (FY) |
1998 – 1999
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| Keywords | Boundary Element Method / BEM / Numerical Analysis / Applied Analysis / Ill-posed Problems / Inverse Problems / Multiprecision Computations / Boundary Integral Equation |
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| Research Abstract |
We deal with mathematical study of convergence and stability for the boundary element method (BEM) as a solver for elliptic boundary value problems. We also give numerical study for our problems, and we develop the computational environment of multiprecision system in the present research.
According to the traditional study for the boundary element method and the boundary integral equation method, we have focused estimation on boundaries in the study of the convergence, but we pointed out the lack of the traditional studies and focused importance of estimation for numerical solution over domains in the first step. We show high accuracy of numerical solutions over domain by BEM, and we clarify one of the merits of BEM in the research. We can observe accurate uniform convergence of numerical solution on a compact set in the domain, and convergence rate in the domain is higher than that on the boundary for smooth data. We also observe, and uniform convergence of numerical solution on a compact set even when numerical solution do not converge uniformly on the boundary. The merit takes advantage in the numerical study for ill-posed problems connected with elliptic partial differential equations.
The research has been carried out separately by each investigator under the control of the head investigator. The head investigator and his research group study numerical experiments of BEM applied to typical elliptic boundary value problems to show high accuracy phenomena of BEM. And they also develop very fast multiprecision system in the present research. The other investigators deal mainly with BEM and others mainly study inverse problems. The multiprecision system developed can be applicable powerfully in the vast fields of numerical analysis.
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