Contribution to a conference proceedings/Contribution to a book

FZJ-2020-01436

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Massively Parallel Multigrid with Direct Coarse Grid Solvers

Huber, M. (Corresponding author)TUM* ; Kohl, N. ; Leleux, P. ; Rüde, U. ; Thönnes, D. ; Wohlmuth, B.TUM*

2020
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich

Please use a persistent id in citations: http://hdl.handle.net/2128/24533

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(10$^{11}$) 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.

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Contributing Institute(s):

1. John von Neumann - Institut für Computing (NIC)

Research Program(s):

1. 899 - ohne Topic (POF3-899) (POF3-899)

Appears in the scientific report 2020

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Linked articles:

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Book/Proceedings Müller, M. (Editor)Extern* ; Binder, K. (Editor) ; Trautmann, A. (Editor)FZJ*
NIC Symposium 2020: proceedings
2020NIC Symposium, JülichJülich, Germany, 27 Feb 2020 - 28 Feb 20202020-02-272020-02-28 Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, NIC Series 50, v, 424 S. (2020)2020   Files  Fulltext by OpenAccess repository BibTeX | EndNote: XML, Text | RIS

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