|arXiv ID:||2203.16069v1||Title:||A unified analysis framework for iterative parallel-in-time algorithms||Language:||English||Authors:||Gander, Martin J.
|Keywords:||Mathematics - Numerical Analysis; Mathematics - Numerical Analysis; Computer Science - Computational Engineering; Finance; and Science; Computer Science - Numerical Analysis||Issue Date:||30-Mar-2022||Source:||arXiv: 2203.16069v1 (2022)||Abstract (english):||
Parallel-in-time integration has been the focus of intensive research efforts over the past two decades due to the advent of massively parallel computer architectures and the scaling limits of purely spatial parallelization. Various iterative parallel-in-time (PinT) algorithms have been proposed, like Parareal, PFASST, MGRIT, and Space-Time Multi-Grid (STMG). These methods have been described using different notations and the convergence estimates that are available for some of them are difficult to compare. We describe Parareal, PFASST, MGRIT and STMG for the Dahlquist model problem using a common notation and give precise convergence estimates using generating functions. This allows us, for the first time, to directly compare their convergence. We prove that all four methods eventually converge super-linearly and compare them directly numerically. Our framework also allows us to find new methods.
|URI:||http://hdl.handle.net/11420/12370||DOI:||10.15480/882.4310||Institute:||Mathematik E-10||Document Type:||Preprint||Project:||TIME parallelisation: for eXascale computing and beyond
|Funded by:||Bundesministerium für Bildung und Forschung (BMBF)
European High-Performance Computing Joint Undertaking (JU)
|More Funding information:||This project has received funding from the European High-Performance Computing Joint Undertaking (JU) under grant agreement No 955701. The JU receives support from the European Union's Horizon 2020 research and innovation programme and Belgium, France, Germany, and Switzerland. This project also received funding from the German Federal Ministry of Education and Research (BMBF) grant 16HPC048.||License:||In Copyright|
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