2004 Fiscal Year Final Research Report Summary
Finite Element Methods for Huge Domain and Domain Decomposition Methods with Related Topics
| Project/Area Number |
14340031
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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 | The University of Electro-Communications |
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Principal Investigator |
USHIJIMA Teruo The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (10012410)
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| Co-Investigator(Kenkyū-buntansha) |
TAKEDA Tatsuoki The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (60272746)
KAKO Takashi The University of Electro-Communications, Faculty of Electro-Communications, Professor, 電気通信学部, 教授 (30012488)
YAMAMOTO Nobito The University of Electro-Communications, Faculty of Electro-Communications, Associate Professor, 電気通信学部, 助教授 (30210545)
TABATA Masahisa Kyusyu University, Department of Mathematical Sciences, Professor, 大学院・数理学研究院, 教授 (30093272)
FUJIMA Shoiti Ibaraki University, Faculty of Science, Associate Professor, 理学部, 助教授 (00209082)
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| Project Period (FY) |
2002 – 2004
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| Keywords | International exchange researchers / Fundamental solution method / 2D exterior reduced wave problems / Conformal mapping of wing / Vocal generation problems / Error estimation constants in FEM / Multi layer neural network / Upwinding technique and method of characteristic curve |
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| Research Abstract |
1.Main Results Obtained in the Joint Works around the Head Investigator :
Demonstration of the possibility for determination of the mapping of wing through finite element computation. Error estimate for the solutions of FSM(=Fundamental Solution Method)approximate problems to reduced wave problems in a domain exterior to a disc. Confirmation of the effectiveness of an FEM-FSM combined method applied to 2D exterior reduced wave problem, and its application to linear water wave problems in an exterior water region with constant water depth, where the abbreviation FEM stands for Finite Element Method.
2.Remarkable Progress Obtained in the Works by Investigators :
(1)Establishment of a method solving linear systems determining discrete vector potentials(by J.Watanabe).
(2)Application of multi layer neural networks to various types of inverse problems(in computer tomography, in data assimilation, in parameter evaluation, in time series prediction)(by T.Takeda).
(3)Application of finite element a
… More
nalysis for stationary wave transmission phenomena in unbounded domains to the problem of voice generation with successfully captured formants(by T.Kako).
(4)Development of a new method for determination of upper bounds for error estimation constants appeared in finite element computation of Poisson equations in non-convex polygonal domains(by N.Yamamoto).
(5)Theoretical study on the effect of stationary non homogeneous spatial structure to qualitative properties of solutions in the case of non-linear reaction-diffusion equations through numerical simulation and asymptotic analysis(by K.Nakamura).
(6)Mathematical and numerically experimental analysis of characteristic futures of approximation methods for various types of partial differential equations obtained through Runge-Kutta type formulas(by T.Koto).
(7)Overcome of the difficulties in finite element numerical solution methods in flow problems through upwinding technique and approximation way of characteristic curves(by M.Tabata).
(8)Finite element analysis of non-stationary field of eddy current based on moving coordinate system(by H.Kanayama).
(9)Flux free finite element method applied to two phase fluid problems(by K Ohmori).
(10)Parallel computation through mortar domain decomposition method(by S.Fujima).
(11)Purely theoretical analysis and numerical analysis of numerical instability problems arising with association of steep change of phenomena, in such as shock waves(by H.aiso).
3.Invitation of Foreign Cooperative Researcher :
(1)Professor Han Hou-de of Applied Mathematics Department, Tsinghua University, Beijing, China from July 26 to August 16,2002.
(2)Professor Yu De-hao of Institute of Mathematics and Scientific/Engineering Computing, Chinese Academy of Sciences, Beijing, China from September 12 to October 3,2004.
4.Research Meetings :
(1)Yokohama Research Meeting was held an KKR Hotel Port Pear Yokohama from January 8 to 10,2003.
(2)Chofu Research Meeting was held at the University of Electro-Communications from February 19 to 20,2004.
(3)Chofu Symposium 2005 was held at the University of Electro-Communication from February 17 to 19,2005. Less
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Research Products
(85 results)
