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

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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)