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

1.主要成果：论证了通过有限元计算确定机翼测绘的可能性。圆盘外区域上约化波动问题的有限单元法近似问题解的误差估计2.研究人员在工作中取得的显著进展：(1)建立了确定离散矢量势的线性系统的方法(由J.Watanabe建立)；(2)多层神经网络在各种反问题中的应用(在计算机层析成像中，在数据同化中，在参数估计中，在时间序列预测中)(T.Takeda)。(3)有限元a…的应用(由T.Takeda)(4)发展了非凸多边形域Poisson方程有限元计算中确定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(K.Nakamura)，从理论上研究了非均匀空间结构对非线性反应扩散方程解的定性性质的影响(K.Nakamura)。由T.Koto的Runge-Kutta型公式得到的各类偏微分方程组的逼近方法的特征展望(7)通过迎风技术和特征曲线的逼近方式克服流动问题中有限元数值方法的困难(M.Tabata)(8)基于移动坐标系的涡流非定常场的有限元分析(H·Kanayama)(9)应用于两相流体问题的无通量有限元方法(K Ohmori)(10)用砂浆区域分解法进行并行计算(S.Fujima)(11)现象急剧变化引起的数值不稳定性问题的纯理论分析和数值分析，3.国外合作研究员邀请：(1)清华大学应用数学系韩厚德教授，中国，2002年7月26日至8月16日。(2)中国科学院数学与科学/工程计算研究所于德教授，北京，中国，2004年9月12日至10月3日。研究会议：(1)横滨研究会议于2003年1月8日至10日在横滨梨港KKR酒店举行。(2)2004年2月19日至20日在电子传媒大学召开调孚研究会议。(3)2005年2月17日至19日在电子传媒大学召开2005年调孚研讨会。较少

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