Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver and Weber, Janine (2019). Preconditioning the coarse problem of BDDC methods - Three-level, algebraic multigrid, and vertex-based preconditioners. Technical Report.

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Abstract

A fair comparison of three Balancing Domain Decomposition by Constraints (BDDC) methods with an approximate coarse space solver is attempted for the first time. The comparison is made for a BDDC method with an algebraic multigrid preconditioner for the coarse problem, a three-level BDDC method, and a BDDC method with a vertex-based coarse preconditioner which was recently introduced by Clark Dohrmann, Kendall Pierson, and Olof Widlund. For the first time, all methods are presented and discussed in a common framework. Condition number bounds are provided for all approaches. All methods are implemented in a common highly parallel scalable BDDC software package based on PETSc, to allow for a fair comparison. Numerical results showing the parallel scalability are presented for the equations of linear elasticity. For the first time, this includes parallel scalability tests for the vertex-based approximate BDDC method.

Item Type:	Preprints, Working Papers or Reports (Technical Report)
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel axel.klawonn@uni-koeln.de orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin martin.lanser@uni-koeln.de UNSPECIFIED UNSPECIFIED Rheinbach, Oliver oliver.rheinbach@math.tu-freiberg.de UNSPECIFIED UNSPECIFIED Weber, Janine janine.weber@uni-koeln.de UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-97138
Series Name at the University of Cologne:	Technical report series. Center for Data and Simulation Science
Volume:	2019,14
Date:	18 June 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 approximate BDDC English three-level BDDC English multilevel BDDC English vertex-based BDDC English
URI:	http://kups.ub.uni-koeln.de/id/eprint/9713