Time Parallel Time Integration

Predicting the future is a difficult task but, as with the weather, it is possible with good models. But how does one predict the far future before the near future is known? Time parallel time integration, also known as PinT (Parallel-in-Time) methods, aims to predict the near and far future simultaneously. In this self-contained book, the first on the topic, readers will find a comprehensive and up-to-date description of methods and techniques that have been developed to do just this. The authors describe the four main classes of PinT methods: shooting-type methods, waveform relaxation methods, time parallel multigrid methods, and direct time parallel methods. In addition, they provide historical background for each of the method classes, complete convergence analyses for the most representative variants of the methods in each class, and illustrations and runnable MATLAB code.

Martin J. Gander is a professor of mathematics at the University of Geneva and was previously a professor of mathematics at McGill University. He has held many visiting professor positions, including the Jean Morlet Chair of the CIRM in fall 2022 and the FSMP Chair in Paris in 2023. He became a SIAM Fellow in 2020. His research interests are numerical analysis and scientific computing, numerical linear algebra and parallel computing, iterative methods and preconditioning, and time parallel time integration.

Thibaut Lunet is a postdoctoral fellow at Hamburg University of Technology. After completing his Ph.D. on time parallelization strategies for numerical simulation of turbulent flows at ISAE-SUPAERO and CERFACS (Toulouse University, France, 2018), he was a postdoctoral fellow with Martin Gander, which led to the genesis of this book. His research interests focus on numerical methods for time integration and parallel computing, numerical analysis and scientific computing, and computational fluid dynamics.