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: | Monograph (Technical Report) |
| Creators: | Creators Email ORCID ORCID Put Code 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 |
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