Time Parallel Time Integration : code repository

This repository contains all the source code (Python, Matlab) associated to the book "Time Parallel Time Integration" (Gander & Lunet 2024), along with corrections of the problem given at the end of each chapters. The folder organization follows the chapter structure of the book, as follow :

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 Iteration 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