Decomposition Methods for Differential Equations: Theory and Applications, 1st Edition (Paperback) book cover

Decomposition Methods for Differential Equations

Theory and Applications, 1st Edition

By Juergen Geiser

CRC Press

304 pages | 43 B/W Illus.

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Description

Decomposition Methods for Differential Equations: Theory and Applications describes the analysis of numerical methods for evolution equations based on temporal and spatial decomposition methods. It covers real-life problems, the underlying decomposition and discretization, the stability and consistency analysis of the decomposition methods, and numerical results.

The book focuses on the modeling of selected multi-physics problems, before introducing decomposition analysis. It presents time and space discretization, temporal decomposition, and the combination of time and spatial decomposition methods for parabolic and hyperbolic equations. The author then applies these methods to numerical problems, including test examples and real-world problems in physical and engineering applications. For the computational results, he uses various software tools, such as MATLAB®, R3T, WIAS-HiTNIHS, and OPERA-SPLITT.

Exploring iterative operator-splitting methods, this book shows how to use higher-order discretization methods to solve differential equations. It discusses decomposition methods and their effectiveness, combination possibility with discretization methods, multi-scaling possibilities, and stability to initial and boundary values problems.

Table of Contents

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

About the Author

Jürgen Geiser is a professor in the Department of Mathematics at Humboldt University of Berlin.

About the Series

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT003000
MATHEMATICS / Applied
MAT007000
MATHEMATICS / Differential Equations
MAT021000
MATHEMATICS / Number Systems