Mathematical Modeling and Numerical Simulation in Continuum Mechanics : Proceedings of the International Symposium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, September 29 – October 3, 2000 Yamaguchi, Japan

This book shows the latest frontiers of the research by the most active researchers in the field of numerical mathematics. The papers in the book were presented in a symposium at Yamaguchi, Japan. The subject of the symposium was mathematical modeling and numerical simulation in continuum mechanics. The topics of the lectures ranged from solids to fluids and included both mathematical and computational analysis of phenomena and algorithms. The readers can study the latest results on shells, plates, flows in various situations, fracture of solids, new ways of exact error estimates and many other topics. Front Matter....Pages I-VIII Nonlinear Shell Models of Koiter’s Type....Pages 1-9 A Survey of Stabilized Plate Elements....Pages 11-21 Prediction of the Fatigue Crack Growth Life in Microelectronics Solder Joints....Pages 23-38 Multi-phase Flow with Reaction....Pages 39-56 Universal and Simultaneous Solution of Solid, Liquid and Gas in Cartesian-Grid-Based CIP Method....Pages 57-71 Subgrid Phenomena and Numerical Schemes....Pages 73-89 Two Scale FEM for Homogenization Problems....Pages 91-107 Numerical Analysis of Electromagnetic Problems....Pages 109-124 A-priori Domain Decomposition of PDE Systems and Applications....Pages 125-135 A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis....Pages 137-153 Essential Spectrum and Mixed Type Finite Element Method....Pages 155-167 Can We Trust the Computational Analysis of Engineering Problems?....Pages 169-183 Numerical Computations for Ill-conditioned Problems by Multiple-Precision Systems....Pages 185-194 Numerical Verification Methods for Solutions of Free Boundary Problems....Pages 195-208 Pattern Formation of Heat Convection Problems....Pages 209-218 Mathematical Modeling and Numerical Simulation of Earth’s Mantle Convection....Pages 219-231 Theoretical and Numerical Analysis on 3-Dimensional Brittle Fracture....Pages 233-251 Exploiting Partial or Complete Geometrical Symmetry in Boundary Integral Equation Formulations of Elastodynamic Problems....Pages 253-269 A New Fast Multipole Boundary Integral Equation Method in Elastostatic Crack Problems in 3D....Pages 271-287 Computational Crack Path Prediction and the Singularities in Elastic-Plastic Stress Fields....Pages 289-301 Back Matter....Pages 303-306 The first international symposium on mathematical foundations of the finite element method was held at the University of Maryland in 1973. During the last three decades there has been great progress in the theory and practice of solving partial differential equations, and research has extended in various directions. Full-scale nonlinear problems have come within the range of nu­ merical simulation. The importance of mathematical modeling and analysis in science and engineering is steadily increasing. In addition, new possibili­ ties of analysing the reliability of computations have appeared. Many other developments have occurred: these are only the most noteworthy. This book is the record of the proceedings of the International Sympo­ sium on Mathematical Modeling and Numerical Simulation in Continuum Mechanics, held in Yamaguchi, Japan from 29 September to 3 October 2000. The topics covered by the symposium ranged from solids to fluids, and in­ cluded both mathematical and computational analysis of phenomena and algorithms. Twenty-one invited talks were delivered at the symposium. This volume includes almost all of them, and expresses aspects of the progress mentioned above. All the papers were individually refereed. We hope that this volume will be a stepping-stone for further developments in this field.

this Book Shows The Latest Frontiers Of The Research By The Most Active Researchers In The Field Of Numerical Mathematics. The Papers In The Book Were Presented At A Symposium Held In Yamaguchi, Japan. The Subject Of The Symposium Was Mathematical Modeling And Numerical Simulation In Continuum Mechanics. The Topics Of The Lectures Ranged From Solids To Fluids And Included Both Mathematical And Computational Analysis Of Phenomena And Algorithms. The Reader Can Study The Latest Results On Shells, Plates, Flows In Various Situations, Fracture Of Solids, New Ways Of Exact Error Estimates And Many Other Topics.