Introduction
Model Problems
Related Models for Decomposition
Examples in Real-Life Applications
Iterative Decomposition of Ordinary Differential Equations
Historical Overview
Decomposition Ideas
Introduction to Classical Splitting Methods
Iterative Splitting Method
Consistency Analysis of the Iterative Splitting Method
Stability Analysis of the Iterative Splitting Method for Bounded Operators
Decomposition Methods for Partial Differential Equations
Iterative Schemes for Unbounded Operators
Computation of the Iterative Splitting Methods: Algorithmic Part
Exponential Runge-Kutta Methods to Compute Iterative Splitting Schemes
Matrix Exponentials to Compute Iterative Splitting Schemes
Algorithms
Extensions of Iterative Splitting Schemes
Embedded Spatial Discretization Methods
Domain Decomposition Methods Based on Iterative Operator Splitting Methods
Successive Approximation for Time-Dependent Operators
Numerical Experiments
Introduction
Benchmark Problems 1: Introduction
Benchmark Problems 2: Comparison with Standard Splitting Methods
Benchmark Problems 3: Extensions to Iterative Splitting Methods
Real-Life Applications
Conclusion to Numerical Experiments: Discussion of Some Delicate Problems
Summary and Perspectives
Software Tools
Software Package Unstructured Grids
Software Package r3t
Solving PDEs Using FIDOS
Appendix
Bibliography
Index
Biography
Juergen Geiser is a researcher in the Department of Mathematics at the Humboldt-University of Berlin. His research interests include numerical and computational analysis, partial differential equations, decomposition and discretization methods for hyperbolic and parabolic equations, optimization, scientific computing, and interface analysis.
