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

大型科学计算数学分析合作研究

• 批准号: 06302016
• 负责人: MIYOSHI T
• 金额: $ 4.22万
• 依托单位: Yamaguchi 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: 1994
• 资助国家: 日本
• 起止时间: 1994 至 1995
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06302016/
• 关键词: Scientific computation; Mathematical modelling; Numerical analysis; Parallel computing; Iteration method; Fluid dynamics; Reaction-Diffusion; Fracture mechanics; 反応一拡散; 数値流体力学; 反応-拡散方程式; 有限要素法; 領域分割法; 反復解法

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)

该项目的目的是发展与科学和工程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 名研究人员获得的众多成果中，与以下主题相关的成果非常突出，并已在期刊或会议论文中发表。 1.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 方法的大收敛性证明 (Yamamoto)，大规模线性系统的预条件高斯-赛德尔方法(Niki)2.流体数学分析N-S方程解的唯一性、分岔和极限(Okamoto)，高精度逆风有限元和三维流体动力学(Tabata)，边界元法的收敛性和稳定性分析(Onishi)，不适定问题的稳定性理论 (Iso)、Steklov 算子的应用 (Ushijima)、多孔介质中的流动分析 (Kawarada)3.反应扩散系统的数值分析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)4.弹性或非弹性体中变形和断裂的数学分析断裂的数学公式 参数（Miyoshi）、三维断裂问题的数学分析（Ohtsuka）

项目成果

Wakano, I.: "Numerical analysis for the wave equation by the boundary element method" Transactions of the Japan S.I.A.M.4-2. 55-65 (1994)

Wakano, I.：“通过边界元法对波动方程进行数值分析”日本汇刊 S.I.A.M.4-2。

Harada, M.: "An extension of the criteria for generalized diagonally dominant matrices" International J.of Computer Math.(accepted).

Harada, M.：“广义对角占优矩阵标准的扩展”International J.of Computer Math.（已接受）。

Fujita, H.: "Distribution theoretic approach to fictitious domain method for Neumann problems" East-West J. Numer. Math.3-2. 111-126 (1995)

Fujita, H.：“诺伊曼问题虚拟域方法的分布理论方法”East-West J. Numer。

Yamamoto, T.: "On nonlinear SOR-like methods, I. -Application to simultaneous methods for polynomial zeros" Japan J. Industrial and Applied Math.(accepted).

Yamamoto, T.：“关于非线性 SOR 类方法，I. -多项式零点联立方法的应用”Japan J. Industrial and Applied Math.（已接受）。

Mimura, M.: "Pattern dynamics in an exotherimic reaction" Physica D. 84. 58-71 (1995)

Mimura, M.：“放热反应中的模式动力学”Physica D. 84. 58-71 (1995)