Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media

Handle URI:
http://hdl.handle.net/10754/625318
Title:
Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media
Authors:
Zampini, Stefano ( 0000-0002-0435-0433 ) ; Tu, Xuemin
Abstract:
Multilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Extreme Computing Research Center
Citation:
Zampini S, Tu X (2017) Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media. SIAM Journal on Scientific Computing 39: A1389–A1415. Available: http://dx.doi.org/10.1137/16m1080653.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Scientific Computing
Issue Date:
3-Aug-2017
DOI:
10.1137/16m1080653
Type:
Article
ISSN:
1064-8275; 1095-7197
Sponsors:
The authors would like to thank the two anonymous referees for their comments and suggestions that helped improve the quality of the manuscript. For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.
Additional Links:
http://epubs.siam.org/doi/10.1137/16M1080653
Appears in Collections:
Articles; Extreme Computing Research Center; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorZampini, Stefanoen
dc.contributor.authorTu, Xueminen
dc.date.accessioned2017-08-10T11:43:34Z-
dc.date.available2017-08-10T11:43:34Z-
dc.date.issued2017-08-03en
dc.identifier.citationZampini S, Tu X (2017) Multilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Media. SIAM Journal on Scientific Computing 39: A1389–A1415. Available: http://dx.doi.org/10.1137/16m1080653.en
dc.identifier.issn1064-8275en
dc.identifier.issn1095-7197en
dc.identifier.doi10.1137/16m1080653en
dc.identifier.urihttp://hdl.handle.net/10754/625318-
dc.description.abstractMultilevel balancing domain decomposition by constraints (BDDC) deluxe algorithms are developed for the saddle point problems arising from mixed formulations of Darcy flow in porous media. In addition to the standard no-net-flux constraints on each face, adaptive primal constraints obtained from the solutions of local generalized eigenvalue problems are included to control the condition number. Special deluxe scaling and local generalized eigenvalue problems are designed in order to make sure that these additional primal variables lie in a benign subspace in which the preconditioned operator is positive definite. The current multilevel theory for BDDC methods for porous media flow is complemented with an efficient algorithm for the computation of the so-called malign part of the solution, which is needed to make sure the rest of the solution can be obtained using the conjugate gradient iterates lying in the benign subspace. We also propose a new technique, based on the Sherman--Morrison formula, that lets us preserve the complexity of the subdomain local solvers. Condition number estimates are provided under certain standard assumptions. Extensive numerical experiments confirm the theoretical estimates; additional numerical results prove the effectiveness of the method with higher order elements and high-contrast problems from real-world applications.en
dc.description.sponsorshipThe authors would like to thank the two anonymous referees for their comments and suggestions that helped improve the quality of the manuscript. For computer time, this research used the resources of the Supercomputing Laboratory at King Abdullah University of Science & Technology (KAUST) in Thuwal, Saudi Arabia.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.relation.urlhttp://epubs.siam.org/doi/10.1137/16M1080653en
dc.rightsArchived with thanks to SIAM Journal on Scientific Computingen
dc.subjectadaptive coarse spaceen
dc.subjectBDDCen
dc.subjectDarcy flowen
dc.subjectdomain decompositionen
dc.subjectPETScen
dc.titleMultilevel Balancing Domain Decomposition by Constraints Deluxe Algorithms with Adaptive Coarse Spaces for Flow in Porous Mediaen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentExtreme Computing Research Centeren
dc.identifier.journalSIAM Journal on Scientific Computingen
dc.eprint.versionPublisher's Version/PDFen
dc.contributor.institutionDepartment of Mathematics, University of Kansas, Lawrence, KS 66045en
kaust.authorZampini, Stefanoen
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