| Project/Area Number |
12440029
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Ehime University |
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Principal Investigator |
AMANO Kaname Faculty of Engineering, Ehime University, Professor, 工学部, 教授 (80113512)
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| Co-Investigator(Kenkyū-buntansha) |
OKANO Dai Faculty of Engineering, Ehime University, Instructors, 工学部, 助手 (90294785)
OGATA Hidenori Faculty of Engineering, Ehime University, Assistant Professors, 工学部, 講師 (50242037)
ITO Hiroshi Faculty of Engineering, Ehime University, Associate Professor, 工学部, 助教授 (90243005)
SUGIHARA Masaaki Department of Computational Science and Engineering, Nagoya University, Professor, 大学院・工学研究科, 教授 (80154483)
YOTSUTANI Shoji Department of Science and Engineering, Ryukoku University, Professor, 理工学部, 教授 (60128361)
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| Project Period (FY) |
2000 – 2002
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| Keywords | charge simulation method / Laplace's equation / fundamental solution / numerical conformal mapping / multiply connected domain / potential problem / complex analysis / numerical analysis |
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| Research Abstract |
The numerical conformal mapping has been an important subject in computational mathematics. On the other hand, the charge simulation method is a simple accurate solver for the Dirichlet problem of the Laplace equation.
1.We have proposed a simple method of numerical conformal mappings of multiply-connected domains onto the canonical domains of Nehari (Mc-Graw Hill, 1952), i.e., (a) the parallel slit domain, (b) the circular slit domain, (c) the radial slit domain, (d) the circle with concentric circular slits and (e) the circular ring with concentric circular slits. The method uses the charge simulation method on the complex plane, i.e., a linear combination of complex logarithmic functions, and gives approximate mapping functions with high accuracy if boundary curves and boundary data are analytic.
2.We have successfully applied the numerical conformal mapping to potential flow analysis, and presented simple methods to find the stagnation points around obstacles and to compute the forces on obstacles.
3.We have presented some techniques to apply the charge simulation method to domains with corners or slits. We also presented new types of the charge simulation method applicable to periodic domains, which use periodic fundamental solutions of the problem instead of logarithmic functions.
4.We proved the unique solvability of the linear systems appearing in the invariant scheme of the charge simulation method.
These results revive the classical method using fundamental solutions as a modern method in the computer age.
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