Universität zu Köln

Heinlein, Alexander ORCID: 0000-0003-1578-8104, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2019). MONOLITHIC OVERLAPPING SCHWARZ DOMAIN DECOMPOSITION METHODS WITH GDSW COARSE SPACES FOR INCOMPRESSIBLE FLUID FLOW PROBLEMS. SIAM J. Sci. Comput., 41 (4). S. C291 - 26. PHILADELPHIA: SIAM PUBLICATIONS. ISSN 1095-7197

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Abstract

Monolithic overlapping Schwarz preconditioners for saddle point problems of Stokes and Navier-Stokes type are presented. In order to obtain numerically scalable algorithms, coarse spaces obtained from the generalized Dryja-Smith-Widlund (GDSW) approach are used. Numerical results of our parallel implementation are presented for various incompressible fluid flow problems. In particular, cases are considered where the problem cannot or should not be reduced using local static condensation, e.g., Stokes or Navier-Stokes problems with continuous pressure spaces. In the new monolithic preconditioners, the local overlapping problems and the coarse problem are saddle point problems with the same structure as the original problem. Our parallel implementation of these preconditioners is based on the fast and robust overlapping Schwarz (FROSch) library, which is part of the Trilinos package ShyLU. The implementation is essentially algebraic in the sense that, for the class of problems presented here, the preconditioners can be constructed from the fully assembled stiffness matrix and information about the block structure of the problem. Further information about the geometry or the null space of the underlying problem can improve the performance compared to the default settings. Parallel scalability results for several thousand cores for Stokes and NavierStokes model problems are reported. Each of the local problems is solved using a direct solver in serial mode, whereas the coarse problem is solved using a direct solver in serial or message passing interface (MPI)-parallel mode or using an MPI-parallel iterative Krylov solver.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander UNSPECIFIED orcid.org/0000-0003-1578-8104 UNSPECIFIED Hochmuth, Christian UNSPECIFIED UNSPECIFIED UNSPECIFIED Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-160686
DOI:	10.1137/18M1184047
Journal or Publication Title:	SIAM J. Sci. Comput.
Volume:	41
Number:	4
Page Range:	S. C291 - 26
Date:	2019
Publisher:	SIAM PUBLICATIONS
Place of Publication:	PHILADELPHIA
ISSN:	1095-7197
Language:	English
Faculty:	Central Institutions / Interdisciplinary Research Centers
Divisions:	Weitere Institute, Arbeits- und Forschungsgruppen > Center for Data and Simulation Science (CDS)
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language NAVIER-STOKES EQUATIONS; SADDLE-POINT PROBLEMS; BLOCK-TRIANGULAR PRECONDITIONERS; FAST ITERATIVE SOLUTION; ALGORITHM; SUBDOMAINS; SOLVERS; INEXACT; NEWTON; GMRES Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/16068