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A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems
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SYSNO ASEP 0468161 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems Author(s) Axelsson, Owe (UGN-S) RID
Blaheta, Radim (UGN-S) RID, SAI, ORCID
Hasal, Martin (UGN-S)Number of authors 3 Source Title High performance computing in science and engineering - HPCSE 2015. - Švýcarsko : Springer, 2016 / Blaheta R. ; Kozubek T. - ISSN 0302-9743 - ISBN 978-3-319-40361-8 Pages s. 68-84 Number of pages 17 s. Publication form Online - E Action International Conference on High Performance Computing in Science and Engineering (HPCSE) /2./ Event date 25.05.2015 - 28.05.2015 VEvent location Soláň Country CZ - Czech Republic Event type EUR Language eng - English Country CH - Switzerland Keywords schur complements ; linear-systems ; high performance computing Subject RIV BA - General Mathematics R&D Projects ED1.1.00/02.0070 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) Institutional support UGN-S - RVO:68145535 UT WOS 000386324600005 EID SCOPUS 84976610827 DOI 10.1007/978-3-319-40361-8_5 Annotation The paper overviews and compares some block preconditioners for the solution of saddle point systems, especially systems arising from the Brinkman model of porous media flow. The considered preconditioners involve different Schur complements as inverse free Schur complement in HSS (Hermitian - Skew Hermitian Splitting preconditioner), Schur complement to the velocity matrix and finally Schur complement to a regularization block in the augmented matrix preconditioner. The inverses appearing in most of the considered Schur complements are approximated by simple sparse approximation techniques as element-by-element and Frobenius norm minimization approaches. A special interest is devoted to problems involving various Darcy, Stokes and Brinkman flow regions, the efficiency of preconditioners in this case is demonstrated by some numerical experiments. Workplace Institute of Geonics Contact Lucie Gurková, lucie.gurkova@ugn.cas.cz, Tel.: 596 979 354 Year of Publishing 2017 Electronic address http://link.springer.com/chapter/10.1007%2F978-3-319-40361-8_5
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