High Order Time Discretization for DAEs with Efficient Block Preconditioners

0482341 - ÚGN 2018 RIV US eng C - Konferenční příspěvek (zahraniční konf.)
Blaheta, Radim - Axelsson, Owe - Luber, Tomáš
High Order Time Discretization for DAEs with Efficient Block Preconditioners.
Proceedings of the international conference on numerical analysis and applied mathematics 2016 (ICNAAM-2016). Melville: American Institute of Physics, 2017, č. článku UNSP 340002-1. AIP Conference Proceedings, 1863. ISBN 978-0-7354-1538-6. ISSN 0094-243X.
[International Conference on Numerical Analysis and Applied Mathematics (ICNAAM). Rhodes (GR), 19.09.2016-25.09.2016]
Grant CEP: GA MŠMT LD15105; GA MŠMT LQ1602
Institucionální podpora: RVO:68145535
Klíčová slova: time dependent partial differential equations (PDEs) * parallelizable preconditioners * two step Radau time integration method
Obor OECD: Applied mathematics
http://aip.scitation.org/doi/abs/10.1063/1.4992509

The contribution considers parabolic PDEs describing uniphysics problems like nonstationary Darcy flow and their
extension to multiphysics like poroelasticity problems. Discretization is assumed by mixed and standard/mixed finite elements
in space and stable higher order methods in time. Parallelizable preconditioners for iterative solution of linear systems arising
within the time steps are suggested and analysed. The analysis shows that the preconditioned systems are diagonalizable with very
localized spectra. It indicates possible very fast convergence of Krylov type methods, which was also confirmed by numerical
experiments with two step Radau time integration method.
Trvalý link: http://hdl.handle.net/11104/0277754