2001 Fiscal Year Final Research Report Summary
Study on non-standard finite element approximation methods for partial differential equations
| Project/Area Number |
11440027
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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 |
KAKO Takashi The University of Electro-Communications, Faculty of Electro-communications, Professor, 電気通信学部, 教授 (30012488)
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| Co-Investigator(Kenkyū-buntansha) |
TABATA Masahisa Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究科, 教授 (30093272)
KAWARADA Hideo Chiba University, Faculty of Engineering, Professor, 工学部, 教授 (90010793)
OHTSUKA Koji Hiroshima Kokusai Gakuin University, Faculty of Engineering, Professor, 工学部, 教授 (30141683)
ZHANG Shao-liang The University of Tokyo, Graduate School of Engineering, Associate Professor, 大学院・工学系研究科, 助教授 (20252273)
NAKAO Mitushiro Kyushu University, Faculty of Mathematics, Professor, 大学院・数理学研究科, 教授 (10136418)
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| Project Period (FY) |
1999 – 2001
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| Keywords | Finite element method / Radiation and scattering problem / Domain decomposition method / Drichlet to Neumann mapping / Fundamental solution method / Earth mantle current / Neutral net computation / Validated computation |
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| Research Abstract |
The following results have been obtained for the non-standard finite element method (FEM) and related problems. The head investigator T. Kako studied the wave propagation in the I exterior unbounded region finding the non-standard finite element approximation method j for a non-local Dirichlet to Neumann mapping, and developed an effective method for 2D radiation problem with high wave number. As an application of the method, it has become possible to compute the formant curve close to the one for the real vowels. He developed the numerical method for the coupling problem between the acoustic field and the structure like shell. He also made clear the importance of the essential Spectrum of the operator in its FEM. The followings are the results by investigators. T. Ushijima studied the fundamental solution method for the 2D reduced wave problem and obtained the convergence and the error estimation. K. Houlka developed the Freeform+ project. H. Kawakawa studied the oil adherence and pen
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etration phenomena on the seashore and obtained its mathematical model and did numerical simulations with various applications.F. Kikuchi developed a new FEM for the plate-bending problem with several numerical examples and studied the efficiency of the Nedelec edge element. D. Koyama studied FEM for the 3D exterior Helmholtz problem combining the fictitious domain method and the Schwarz alternative method. T. Takeda and M. Fukuhara developed the structured neural network method for partial differential equations. M. Tabata found the new FEM scheme for earth mantle convection problem with error estimation. S. -L. Zhang studied various conjugate gradient type method for linear equations. T. Miyoshi found a criterion to determine the direction of a crack extension. M. Nakao and N. Yamamoto studied the validated numerical method for FEM computation and developed the method to evaluate the approximation property of FEM with validation by reducing the problem to the generalized matrix eigenvalue problem. Less
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