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Decomposition Methods for Differential Equations

Theory and Applications

Decomposition Methods for Differential Equations by Juergen Geiser
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Preface

Introduction

Modeling: Multi-Physics Problems

Introduction

Models for Multi-Physics Problems

Examples for Multi-Physics Problems

Abstract Decomposition and Discretization Methods

Decomposition

Discretization

Time-Decomposition Methods for Parabolic Equations

Introduction for the Splitting Methods

Iterative Operator-Splitting Methods for Bounded Operators

Iterative Operator-Splitting Methods for Unbounded Operators

Decomposition Methods for Hyperbolic Equations

Introduction for the Splitting Methods

ADI Methods and LOD Methods

Iterative Operator-Splitting Methods for Wave Equations

Parallelization of Time Decomposition Methods

Nonlinear Iterative Operator-Splitting Methods

Spatial Decomposition Methods

Domain Decomposition Methods Based on Iterative Operator-Splitting Methods

Schwarz Waveform-Relaxation Methods

Overlapping Schwarz Waveform Relaxation for the Solution of Convection-Diffusion-Reaction Equation

Numerical Experiments

Introduction

Benchmark Problems for the Time Decomposition Methods for Ordinary Differential and Parabolic Equations

Benchmark Problems for Spatial Decomposition Methods: Schwarz Waveform-Relaxation Method

Benchmark Problems: Hyperbolic Equations

Real-Life Applications

Summary and Perspectives

Notation

Appendix A: Software Tools

Appendix B: Discretization Methods

Literature

References

Index

CRC Press; May 2009
320 pages; ISBN 9781439810972
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Title: Decomposition Methods for Differential Equations
Author: Juergen Geiser
 
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