1st Edition
Decomposition Methods for Differential Equations Theory and Applications
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
Biography
Jürgen Geiser is a professor in the Department of Mathematics at Humboldt University of Berlin.
