Universität zu Köln

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2019). Reduced Dimension GDSW Coarse Spaces for Monolithic Schwarz Domain Decomposition Methods for Incompressible Fluid Flow Problems. Technical Report.

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Abstract

Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared to preconditioners based on incomplete block factorizations. However, the computational costs for the setup and the application of monolithic preconditioners are typically higher. In this paper, several techniques to further improve the convergence speed as well as the computing time are applied to monolithic two-level Generalized Dryja–Smith–Widlund (GDSW) preconditioners. In particular, reduced dimension GDSW (RGDSW) coarse spaces, restricted and scaled versions of the first level, hybrid and parallel coupling of the levels, and recycling strategies are investigated. Using a combination of all these improvements, for a small time-dependent Navier-Stokes problem on 240 MPI ranks, a reduction of 86 % of the time-to-solution can be obtained. Even without applying recycling strategies, the time-to-solution can be reduced by more than 50% for a larger steady Stokes problem on 4 608 MPI ranks. For the largest problems with 11979 MPI ranks the scalability deteriorates drastically for the monolithic GDSW coarse space. On the other hand, using the reduced dimension coarse spaces, good scalability up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, could be achieved.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander alexander.heinlein@uni-koeln.de orcid.org/0000-0003-1578-8104 UNSPECIFIED Hochmuth, Christian christian.hochmuth@uni-koeln.de UNSPECIFIED UNSPECIFIED Klawonn, Axel axel.klawonn@uni-koeln.de orcid.org/0000-0003-4765-7387 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-96753
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2019,12
Date:	30 May 2019
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	Data processing Computer science Natural sciences and mathematics Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language domain decomposition English overlapping Schwarz English reduced dimension coarse space English GDSW English algebraic preconditioner English parallel computing English incompressible fluids English Stokes English Navier-Stokes English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9675