Schur complement-schwarz DD preconditioners for non-stationary darcy flow problems

0495505 - ÚGN 2019 RIV CH eng C - Conference Paper (international conference)
Blaheta, Radim - Kružík, Jakub - Luber, Tomáš
Schur complement-schwarz DD preconditioners for non-stationary darcy flow problems.
High Performance Computing in Science and Engineering - HPCSE 2017. Cham: Springer, 2018 - (Kozubek, T.; Čermák, M.; Tichý, P.; Blaheta, R.; Šístek, J.; Lukáš, D.; Jaroš, J.), s. 59-72. Lecture Notes in Computer Science, 11087. ISBN 978-3-319-97135-3. ISSN 0302-9743.
[HPCSE 2017: International Conference on High Performance Computing in Science and Engineering /3./. Karolinka (CZ), 22.05.2017-25.05.2017]
R&D Projects: GA MŠMT LQ1602; GA MŠMT LD15105
Grant - others:GA ČR(CZ) GA15-18274S
Institutional support: RVO:68145535
Keywords : preconditioner * saddle point problems * singular saddle
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
https://link.springer.com/content/pdf/10.1007%2F978-3-319-97136-0_5.pdf

The paper concerns development of highly parallelizable preconditioners for solving nonstationary Darcy flow problems. The discretization of the solved problem is done by mixed finite elements in space and by first order implicit Euler discretization in time. The systems with generalized saddle point matrices, which appear in each time step of the implicit Euler method, are then solved by FGMRES method
with a block type preconditioner. Moreover, highly parallelizable, one-level additive Schwarz method is used for preconditioning of the velocity
block. Both analysis and numerical experiment show that this application of the Schwarz method is highly efficient for a class of flow problems with parameters corresponding to many applications in geosciences.
Permanent Link: http://hdl.handle.net/11104/0288473