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Heinlein, Alexander, Hochmuth, Christian and Klawonn, Axel ORCID: 0000-0003-4765-7387 (2018). Monolithic Overlapping Schwarz Domain Decomposition Methods with GDSW Coarse Spaces for Saddle Point Problems. Technical Report.

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Abstract

Monolithic overlapping Schwarz preconditioners for saddle point problems of Stokes, Navier-Stokes, and mixed linear elasticity ty e are presented. For the first time, coarse spaces obtained from the GDSW (Generalized Dryja-Smith-Widlund) approach are used in such a setting. Numerical results of our parallel implementation are presented for several model problems. In particular, cases are considered where the problem cannot or should not b e reduced using local static condensation, e.g., Stokes, Navier-Stokes or mixed elasticity 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 FROSch (Fast and Robust Overlapping Schwarz) library, which is part of the Trilinos package ShyLU. The implementation is algebraic in the sense that the preconditioners can be constructed from the fully assembled stiffness matrix and information about the block structure of the problem. Parallel scalability results for several thousand cores for Stokes, Navier-Stokes, and mixed linear elasticity model problems are reported. Each of the local problems is solved using a direct solver in serial mo de, whereas the coarse problem is solved using a direct solver in serial or MPI-parallel mode or using an MPI-parallel iterative Krylov solver

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Heinlein, Alexander alexander.heinlein@uni-koeln.de UNSPECIFIED 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:38-83431
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2018,1
Number of Pages:	27
Date:	2 July 2018
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 Mathematics Technology (Applied sciences)
Uncontrolled Keywords:	Keywords Language monolithic overlapping Schwarz English domain decomposition English saddle point problem English Stokes English Navier-Stokes English GDSW English parallel computing English algebraic preconditioner English
Funders:	Deutsche Forschungsgemeinschaft
Projects:	Domain-Decomposition-Based Fluid Structure Interaction Algorithms for Highly Nonlinear and Anisotropic Elastic Arterial Wall Models in 3D
URI:	http://kups.ub.uni-koeln.de/id/eprint/8355