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

为了解决非线性现象及其动态的结构，本研究项目已涉及以下五个主要领域：（1）流体动态中的非线性结构，（2）自由边界的动态，（3）分裂现象的科学计算，（4）在不同方程式中出现在bifurcations.im.im中的方程式中，（4）奇异点出现在不同方程式中。自动导向车辆（TABATA）周围的空气流量计算，轴心流动问题的有限元分析（TABATA），有限深度（Okamoto）进行性波的分叉，背景剪切流中的涡流板卷起（Okamoto）中的涡流板以及具有单一边界条件的流动问题（Fujita）。 Pattern selections for two breathers (Ikeda and Nishiura), Global bifurcation diagram of travel 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媒体（2）中的媒体（Kawarada）。弹性塑料问题的任意线方法（Miyoshi）和（3）中改进的4节点四边形板弯曲元件（kikuchi）。（4）中退化抛物线方程（Tsutsumi和Matano）的爆炸问题。反应扩散系统和惯性歧管（Morita）和Navier-Stokes在（5）中流动倾斜板（Nishida）。例如，其他相关主题也是研究的，大脑动力学（FUJII）以及混乱理论在社会科学（Yamaguti）中的应用。目前的项目的特征是与数值计算合作的数学分析。数值方法的发展领域已获得以下结果：用于大型线性方程式（MITSUI）的共轭梯度方法（MITSUI），正交公式，用于可变转换（MORI）获得的傅立叶类型积分（MORI），计算机有助于计算机的证明，用于在流体动力学方程（nishIDA）方程中的分化方法（nishIDA）方程中的分类问题（nishIDA）的依赖性依据（nishida）的构造率（nishIDA）。例如（富士）。较少的