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| :: Table of Contents |
Chapter 1. Introduction
1.1 Weather Prediction as an Example
1.2 Ordinary Differential Equations (ODEs)
1.3 Partial Differential Equations (PDEs)
1.4 Historical Overview
1.5 Problems
Chapter 2. Multiple Shooting Type Methods
2.1 Idea of Nievergelt in 1964
2.2 Multiple Shooting Methods in Time
2.3 The Parareal Algorithm
2.4 Problems
Chapter 3. Waveform Relaxation and Domain Decomposition
3.1 Method of Successive Approximations
3.2 Classical Waveform Relaxation
3.3 Waveform Relaxation Based on Domain Decomposition
3.4 Optimized Schwarz Waveform Relaxation
3.5 Problems
Chapter 4. Time Multigrid Methods
4.1 Time Parallel Time Stepping
4.2 Parabolic Multigrid
4.3 Time Multigrid for the Dahlquist Equation
4.4 Space Time Multigrid Methods
4.5 MultiGrid Reduction In Time
4.6 Block Iterations and Generating Functions
4.7 Parallel Full Approximation Scheme in Space-Time
4.8 Problems
Chapter 5. Direct Space Time Parallel Solvers
5.1 Parallel Predictor Corrector Methods
5.2 Boundary Value Methods
5.3 Time Parallel Cyclic Reduction
5.4 Time Parallel Methods Based on Laplace Transform
5.5 Time Parallelization Based on Diagonalization
5.6 Time Parallelization Based on Integral Deferred Corrections
5.7 ParaExp
5.8 Problems
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