A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems

0468161 - ÚGN 2017 RIV CH eng C - Konferenční příspěvek (zahraniční konf.)
Axelsson, Owe - Blaheta, Radim - Hasal, Martin
A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems.
High performance computing in science and engineering - HPCSE 2015. Švýcarsko: Springer, 2016 - (Blaheta, R.; Kozubek, T.), s. 68-84. Lecture Notes in Computer Science, 9611. ISBN 978-3-319-40361-8. ISSN 0302-9743.
[International Conference on High Performance Computing in Science and Engineering (HPCSE) /2./. Soláň (CZ), 25.05.2015-28.05.2015]
Grant CEP: GA MŠMT ED1.1.00/02.0070
Institucionální podpora: RVO:68145535
Klíčová slova: schur complements * linear-systems * high performance computing
Kód oboru RIV: BA - Obecná matematika
http://link.springer.com/chapter/10.1007%2F978-3-319-40361-8_5

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.
Trvalý link: http://hdl.handle.net/11104/0266018