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:
CreatorsEmailORCID
Klawonn, Axelaxel.klawonn@uni-koeln.deorcid.org/0000-0003-4765-7387
Lanser, Martinmartin.lanser@uni-koeln.deUNSPECIFIED
Rheinbach, Oliveroliver.rheinbach@math.tu-freiberg.deUNSPECIFIED
Weber, Janinejanine.weber@uni-koeln.deUNSPECIFIED
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
Subjects: Data processing Computer science
Natural sciences and mathematics
Mathematics
Technology (Applied sciences)
Uncontrolled Keywords:
KeywordsLanguage
approximate BDDCEnglish
three-level BDDCEnglish
multilevel BDDCEnglish
vertex-based BDDCEnglish
Faculty: Central Institutions / Interdisciplinary Research Centers
Divisions: Central Institutions / Interdisciplinary Research Centers > Center for Data and Simulation Science
Language: English
Date: 18 June 2019
URI: http://kups.ub.uni-koeln.de/id/eprint/9713

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