BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields
dc.contributor.author | Oh, Duk-Soon | |
dc.contributor.author | Widlund, Olof B. | |
dc.contributor.author | Zampini, Stefano | |
dc.contributor.author | Dohrmann, Clark R. | |
dc.date.accessioned | 2018-02-01T07:24:59Z | |
dc.date.available | 2018-02-01T07:24:59Z | |
dc.date.issued | 2017-06-13 | |
dc.identifier.citation | Oh D-S, Widlund OB, Zampini S, Dohrmann CR (2017) BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields. Mathematics of Computation 87: 659–692. Available: http://dx.doi.org/10.1090/mcom/3254. | |
dc.identifier.issn | 0025-5718 | |
dc.identifier.issn | 1088-6842 | |
dc.identifier.doi | 10.1090/mcom/3254 | |
dc.identifier.uri | http://hdl.handle.net/10754/626963 | |
dc.description.abstract | A BDDC domain decomposition preconditioner is defined by a coarse component, expressed in terms of primal constraints, a weighted average across the interface between the subdomains, and local components given in terms of solvers of local subdomain problems. BDDC methods for vector field problems discretized with Raviart-Thomas finite elements are introduced. The methods are based on a deluxe type of weighted average and an adaptive selection of primal constraints developed to deal with coefficients with high contrast even inside individual subdomains. For problems with very many subdomains, a third level of the preconditioner is introduced. | |
dc.description.abstract | Under the assumption that the subdomains are all built from elements of a coarse triangulation of the given domain, that the meshes of each subdomain are quasi uniform and that the material parameters are constant in each subdomain, a bound is obtained for the condition number of the preconditioned linear system which is independent of the values and the jumps of these parameters across the interface between the subdomains as well as the number of subdomains. Numerical experiments, using the PETSc library, are also presented which support the theory and show the effectiveness of the algorithms even for problems not covered by the theory. Included are also experiments with Brezzi-Douglas-Marini finite element approximations. | |
dc.description.sponsorship | The work of the second author was supported in part by the National Science Foundation Grants DMS-1216564 and DMS-1522736. | |
dc.publisher | American Mathematical Society (AMS) | |
dc.relation.url | http://www.ams.org/journals/mcom/2018-87-310/S0025-5718-2017-03254-3/ | |
dc.relation.url | http://pdfs.semanticscholar.org/7f30/d140685d86602011a72826317fbe3f81d8fc.pdf | |
dc.rights | First published in Mathematics of Computation in Volume 87, Number 310, March 2018, Pages 659–692, published by the American Mathematical Society | |
dc.rights | This file is an open access version redistributed from: http://pdfs.semanticscholar.org/7f30/d140685d86602011a72826317fbe3f81d8fc.pdf | |
dc.subject | Domain decomposition | |
dc.subject | BDDC preconditioner | |
dc.subject | Raviart-Thomas finite elements | |
dc.subject | multilevel preconditioners | |
dc.subject | adaptive selection of coarse spaces | |
dc.title | BDDC Algorithms with deluxe scaling and adaptive selection of primal constraints for Raviart-Thomas vector fields | |
dc.type | Article | |
dc.contributor.department | Extreme Computing Research Center | |
dc.contributor.department | Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division | |
dc.identifier.journal | Mathematics of Computation | |
dc.eprint.version | Post-print | |
dc.contributor.institution | Department of Mathematics, Rutgers University, Piscataway, NJ, 08854, , United States | |
dc.contributor.institution | Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY, 10012, , United States | |
dc.contributor.institution | Computational Solid Mechanics and Structural Dynamics, Sandia National Laboratories, Albuquerque, NM, 87185, , United States | |
kaust.person | Zampini, Stefano | |
refterms.dateFOA | 2020-06-30T13:52:38Z | |
dc.date.published-online | 2017-06-13 | |
dc.date.published-print | 2017-06-21 |