Mathematical Modeling and Numerical Simulation in Continuum Mechanics

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.

Klappentext

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.

Inhalt

Nonlinear Shell Models of Koiter's Type.- A Survey of Stabilized Plate Elements.- Prediction of the Fatigue Crack Growth Life in Microelectronics Solder Joints.- Multi-phase Flow with Reaction.- Universal and Simultaneous Solution of Solid, Liquid and Gas in Cartesian-Grid-Based CIP Method.- Subgrid Phenomena and Numerical Schemes.- Two Scale FEM for Homogenization Problems.- Numerical Analysis of Electromagnetic Problems.- A-priori Domain Decomposition of PDE Systems and Applications.- A One Dimensional Model for Blood Flow: Application to Vascular Prosthesis.- Essential Spectrum and Mixed Type Finite Element Method.- Can We Trust the Computational Analysis of Engineering Problems?.- Numerical Computations for Ill-conditioned Problems by Multiple-Precision Systems.- Numerical Verification Methods for Solutions of Free Boundary Problems.- Pattern Formation of Heat Convection Problems.- Mathematical Modeling and Numerical Simulation of Earth's Mantle Convection.- Theoretical and Numerical Analysis on 3-Dimensional Brittle Fracture.- Exploiting Partial or Complete Geometrical Symmetry in Boundary Integral Equation Formulations of Elastodynamic Problems.- A New Fast Multipole Boundary Integral Equation Method in Elastostatic Crack Problems in 3D.- Computational Crack Path Prediction and the Singularities in Elastic-Plastic Stress Fields.