Improving the Efficiency and Theoretical Understanding of Time-Parallel Multigrid Methods

Diplôme Thèse Improving the Efficiency and Theoretical Understanding of Time-Parallel Multigrid Methods eng 2025-05-13 2025-05-13 author Bronasco Ausra 817545 director Gander Martin Jakob 134664 Section de mathématiques (MATH) 146 10.13097/archive-ouverte/unige:187048 urn:nbn:ch:unige-1870483 Sc. 5910 Clusters worldwide have millions of cores. It is important to develop algorithms that can fully use those resources. Parallel-in-time algorithms parallelize simulations by taking advantage of additional cores to start computing the solution at a later time, even if the solution at the current time has not been computed yet. We study three algorithms: one which is easy to use, Parareal, and a variant with more layers of computation, Multigrid Reduction-in-Time, as well as a more performant one, Space-Time Multigrid. We analyze their convergence properties to make them more efficient and to better understand them. Les clusters du monde entier ont des millions de processeurs. Il est donc important de développer des algorithmes qui utilisent ces ressources de manière efficace. Les algorithmes de parallélisme en temps utilisent davantage de processeurs pour pouvoir calculer la solution d'un problème à temps plus lointain sans avoir fini de calculer la solution à un temps plus proche. Nous étudions trois algorithmes : un qui est facile à utiliser, Pararéel, et une de ses variantes à plusieurs niveaux, Multigrid Reduction-in-Time, ainsi qu'un algorithme plus performant, Space-Time Multigrid. Nous analysons la convergence de ces algorithmes pour les rendre plus efficaces et pour mieux les comprendre. Parallel computing High performance computing Time-parallel Partial differential equations Pdes Parallel-in-time Runge-kutta methods Spatial coarsening Multigrid Multilevel Parareal Mgrit Stmg Dewey 510 25 Section de mathématiques 11 false 847 Analyse numérique fd698559-7351-4fa9-9ea5-62eec96e8c8f Thesis Public main.pdf 3931002 application/pdf 7f42e076af2add9347ce291169aad4a94da226f23fea98f0955b37146341daae 0370c42e-eb69-4eab-a4e3-b5cc0ea8ea88 Imprimatur Public imprimatur.pdf 690979 application/pdf c30463687549e9da5601a1164bcf88cf1cab2e639b0e63bbc2fe0636615d2333 openAccess Faculté des sciences / Section de mathématiques

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Improving the Efficiency and Theoretical Understanding of Time-Parallel Multigrid Methods				2025	168	213

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