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

1.主要研究成果：通过有限元计算确定机翼映射的可能性。在圆盘外的区域内，将FSM（=基本解方法）近似问题的解近似为约化波问题的解的误差估计。验证了FEM-FSM组合方法应用于二维外部约化波浪问题的有效性，并将其应用于具有恒定水深的外部水域中的线性水波问题，其中缩写FEM代表有限元方法。2.研究人员在工作中取得的显著进展：（1）建立了求解线性系统的方法，确定了离散矢量势（J. Watanabe）。（2）多层神经网络在各种逆问题中的应用（计算机层析成像、数据同化、参数评估、时间序列预测）（T.Takeda）。（3）有限元法的应用 ...更多信息 对无界域中驻波传输现象的分析，以及成功捕获共振峰的语音生成问题（T. Kako）。（4）提出了一种确定非凸多边形区域上Poisson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研究了非线性反应扩散方程定常非齐次空间结构对解的定性性质的影响（K.中村）。（6）通过Runge-Kutta型公式（T. Koto）获得的各种类型的偏微分方程的近似方法的特征性质的数学和数值实验分析。（7）利用迎风技术和特征曲线逼近方法克服了流动问题有限元数值解法的困难（M. Tabata）。（8）基于移动坐标系的涡流非稳态场的有限元分析（H. Kanayama）。（9）两相流体问题的无通量有限元法（K Ohmori）。（10）通过砂浆区域分解方法的并行计算（S. Fujima）。（11）冲击波等陡变现象引起的数值不稳定性问题的理论分析和数值分析（H. aiso）。3.邀请国外合作研究者：（1）清华大学应用数学系韩厚德教授于2002年7月26日至8月16日在中国北京。（2）于德浩教授，中国科学院数学与科学/工程计算研究所，北京，2004年9月12日至10月3日。4.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饭店举行。（2）乔夫研究会议于2004年2月19日至20日在电子通信大学举行。（3）乔夫研讨会2005于2005年2月17日至19日在电子通信大学举行。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