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Decomposition Methods for Differential Equations: Theory and Applications

Juergen Geiser
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2009
Number of Pages: 
294
Format: 
Hardcover
Series: 
Chapman & Hall/CRC Numerical Analysis and Scientific Computing
Price: 
89.95
ISBN: 
9781439810965
Category: 
Monograph
We do not plan to review this book.

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

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