Co-operative Research on the Mathematical Analysis of Large Scientific Computation

该项目的目的是发展与科学和工程中的数学建模相关的大规模科学计算的数学理论。该项目由以下四组组成。在该项目的14位研究者所取得的众多成果中，与以下主题相关的成果较为突出，并已在期刊或论文集上发表。2.大规模线性或非线性系统的并行或/和迭代计算同伦方法在大规模特征值问题中的应用（shimasaki），非线性系统的SOR型Durand-Kerner方法的大收敛证明（Yamamoto），大规模线性系统的预条件高斯-塞德尔方法（Niki）3.流体的数学分析N-S方程解的唯一性、分岔和极限（Okamoto），高精度和三维流体动力学的迎风有限元法（Tabata），边界元法的收敛性和稳定性分析（Onishi），病态问题的稳定性理论（Iso）， Steklov算子的应用（Ushijima），多孔介质的流动分析（Kawarada）。反应扩散系统中的模式动力学（Mimura），化学界面反应的数学模型（Yotsutani）弹性或非弹性体变形和断裂的数学分析断裂参数的数学公式（Miyoshi），三维断裂问题的数学分析（Ohtsuka）

The aim of this project is to develope the mathematical theory of large scale scientific computation related to the mathematical modelling in science and engineering. The project consists of the following four groups. Among many results obtained by the 14 investigators of the project, those related to the following topics are outstanding and already published in journals or proceedings.1.Parallel or/and iterative computation for large scale linear or non-linear systemsApplication of homotopy method to large scale eigen-value problems (shimasaki), Proof of the convergence in-large of a SOR type Durand-Kerner method for non-linear systems (Yamamoto), Pre-conditioned Gauss-Seidel method for large scale linear systems (Niki)2.Mathematical analysis of fluidUniqueness, bifurcation and limit of the solutions of N-S equations (Okamoto), Upwind FEM with high accuracy and three-dimensional fluid dynamics (Tabata), Convergence and stability analysis of BEM (Onishi), Stability theory of ill-posed problems (Iso), Application of Steklov operator (Ushijima), Analysis of flow in porous media (Kawarada)3.Numerical analysis of reaction-diffusion systemsPattern dynamics in reaction-diffusion systems (Mimura), Mathematical models of Chemical interfacial reaction (Yotsutani)4.Mathematical analysis of deformation and fracture in elastic or non-elastic bodiesMathematical formulations of fracture parameters (Miyoshi), Mathematical Analysis of three-dimensional fracture problems (Ohtsuka)