Analysis and Computation of Nonlinear Structures

非线性结构分析与计算

基本信息

批准号：
05302013
负责人：
IKEDA Tsutomu
金额：
$ 9.86万
依托单位：
Ryukoku University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Co-operative Research (A)
财政年份：
1993
资助国家：
日本
起止时间：
1993 至 1995
项目状态：
已结题

项目摘要

For the purpose of solving the structure of nonlinear phenomena and their dynamics, the present research project has been dealt with the following five major fields : (1) Nonlinear structure in fluid dynamics, (2) Dynamics of free boundaries, (3) Scientific computing of fracture phenomena, (4) Singular points appearing in differential equations, (5) Tracking of bifurcation structure.Important results are as follows. Air flow computation around an automated guided vehicle (Tabata), Finite element analysis of axisymmetric flow problems (Tabata), Bifurcation of progressive waves of finite depth (Okamoto), Vortex sheet roll-up in the background shear flow (Okamoto) and Flow problems with unilateral boundary conditions (Fujita). Pattern selections for two breathers (Ikeda and Nishiura), Global bifurcation diagram of traveling pulses (Ikeda), Existence and stability of interfacial patterns in higher dimensional spaces (Nishiura), Singular limit systems derived from reaction-diffusion systems … More (Mimura), Numerical computation of generalized curve shortening equations (Tsutsumi) and Free boundaries in porous media (Kawarada) in (2). The arbitrary line method for elasto-plastic problems (Miyoshi) and Improved 4-node quadrilateral plate bending element (Kikuchi) in (3). Blow-up problems of degenerate parabolic equations (Tsutsumi and Matano) in (4). Reaction-diffusion systems and inertial manifolds (Morita) and Navier-Stokes flows down an inclined plate (Nishida) in (5). Other related topics have been also studied, Brain dynamics (Fujii) and Application of chaos theory to social sciences (Yamaguti) for instance.The present project is characterized by the mathematical analysis in cooperation with numerical computation. The following results have been obtained in the field of the development of numerical methods : An improved conjugate gradient method for large systems of linear equations (Mitsui), Quadrature formulas for Fourier type integrals obtained by variable transformation (Mori), Computer aided proofs for bifurcation problems in equations of fluid dynamics (Nishida) and The domain dependence of convergence rate of a domain decomposition method (Fujita) for instance. Less

为了求解非纤维菌和动力学，预言项目是Ajor领域：（1）流体动力学中的非线性结构，（2）自由边界的动力学，（3）裂缝现象的科学计算，（4）奇异点在微分方程中，跟踪分叉结构。最重要的结果如下。和nishiura）的脉冲（Ikeda），较高的Dimesional空间中界面模式的存在和稳定性（Nishiura）Om反应 - 扩散系统…更多（Mimura），广义曲线缩短方程（Mimura）的数值计算（Mimerical），以及在多孔介质中的自由媒体中的自由介质（Kawarada）在（2）中。 Navier-Stokes在（5）中还研究了倾斜的板块（Nishida）。在iCal计算中，在数值方法的开发中得出了以下结果：改进的线性方程式（MITSUI）的共轭方法，通过变量转换（MORI）在流体动力学方程（NishIDAS）中获得的正交公式四式积分。例如，域分解方法（Fujita）的收敛依赖性