Massively Parallel Multigrid with Direct Coarse Grid Solvers

Huber M, Kohl N, Leleux P, Rüde U, Thönnes D, Wohlmuth B (2020)

Publication Language: English

Publication Type: Conference contribution, Conference Contribution

Publication year: 2020

Series: NIC Series

Conference Proceedings Title: NIC Symposium 2020

Event location: Forschungszentrum Jülich John von Neumann Institute for Computing (NIC) DE

ISBN: 978-3-95806-443-0

Abstract

Multigrid methods play an important role in the numerical approximation of partial differential equations. As long as only a moderate number of processors is used, many alternatives can be used as solver for the coarsest grid. However, when the number of processors increases, then standard coarsening will stop while the problem is still large and the communication overhead for solving the corresponding coarsest grid problem may dominate. In this case, the coarsest grid must be agglomerated to only a subset of the processors. This article studies the use of sparse direct methods for solving the coarsest grid problem as it arises in a multigrid hierarchy. We use as test case a Stokes-type model and solve algebraic saddle point systems with up to O(1011) degrees of freedom on a current peta-scale supercomputer. We compare the sparse direct solver with a preconditioned minimal residual iteration and show that the sparse direct method can exhibit better parallel efficiency

Authors with CRIS profile

Nils Kohl Lehrstuhl für Informatik 10 (Systemsimulation) Ulrich Rüde Lehrstuhl für Informatik 10 (Systemsimulation) Dominik Thönnes Lehrstuhl für Informatik 10 (Systemsimulation)

Involved external institutions

Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique (CERFACS) FR France (FR) Technische Universität München (TUM) DE Germany (DE)

How to cite

APA:

Huber, M., Kohl, N., Leleux, P., Rüde, U., Thönnes, D., & Wohlmuth, B. (2020). Massively Parallel Multigrid with Direct Coarse Grid Solvers. In NIC Symposium 2020. Forschungszentrum Jülich John von Neumann Institute for Computing (NIC), DE.

MLA:

Huber, Markus, et al. "Massively Parallel Multigrid with Direct Coarse Grid Solvers." Proceedings of the NIC Symposium 2020, Forschungszentrum Jülich John von Neumann Institute for Computing (NIC) 2020.

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