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

Conference paper

DOI: 10.1007/978-3-319-40361-8_5

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9611)
Cite this paper as:
Axelsson O., Blaheta R., Hasal M. (2016) A Comparison of Preconditioning Methods for Saddle Point Problems with an Application to Porous Media Flow Problems. In: Kozubek T., Blaheta R., Šístek J., Rozložník M., Čermák M. (eds) High Performance Computing in Science and Engineering. HPCSE 2015. Lecture Notes in Computer Science, vol 9611. Springer, Cham

Abstract

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.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institute of Geonics AS CROstrava-PorubaCzech Republic

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