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Finite Element Methods for Huge Domain and Domain Decomposition Methods with Related Topics

巨大域的有限元方法和相关主题的域分解方法

基本信息

批准号：
14340031
负责人：
USHIJIMA Teruo
金额：
$ 8.19万
依托单位：
The University of Electro-Communications
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2004
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-14340031/
关键词：
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

项目摘要

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

1.在首席调查员周围的联合工作中获得的主要结果：论证了通过有限元计算确定机翼映射的可能性。圆盘外域内简化波问题的FSM（=基本解法）近似问题解的误差估计验证了FEM- fsm组合方法在二维外化简波问题中的有效性，并将其应用于恒定水深外水域的线性水波问题，其中FEM为Finite Element method的缩写。研究者的工作取得了显著进展：(1)建立了求解线性系统确定离散向量势的方法（渡边j）。(2)多层神经网络在各类反问题（计算机断层扫描、数据同化、参数评估、时间序列预测）中的应用（T.Takeda）。(3)有限元的应用[a] .在成功捕获共振峰的语音生成问题上对无界域中驻波传输现象的更多分析[T.Kako]。(4)提出了一种确定非凸多边形域泊松方程有限元计算中误差估计常数上界的新方法（N.Yamamoto）。(5)通过数值模拟和渐近分析理论研究了平稳非齐次空间结构对非线性反应扩散方程解定性性质的影响（K.Nakamura）。(6)通过龙格-库塔型公式得到的各种类型偏微分方程的近似方法的特征期货的数学和数值实验分析（T.Koto）。(7)利用上绕技术和特征曲线逼近方法克服了流动问题有限元数值求解方法的难点（m.b abata）。(8)基于运动坐标系的涡流非定常场有限元分析（H.Kanayama）。(9)应用于两相流体问题的无通量有限元法（K Ohmori）。（10）通过砂浆域分解方法并行计算（S.Fujima）。（11）对激波等急剧变化现象所引起的数值不稳定性问题的纯理论分析和数值分析。(1)清华大学应用数学系韩厚德教授，2002年7月26日至8月16日，中国北京。(2)余德豪教授，中国科学院数学与科学/工程计算研究所，中国北京，2004.9.12—2004.10.3。研究会议：(1)横滨研究会议于2003年1月8日至10日在横滨港梨KKR酒店召开。(2) 2004年2月19日至20日在中国电子通信大学召开了中央研究院学术会议。(3) 2005年2月17日至19日在中国电子通信大学召开了“2005秋布学术研讨会”。少