Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 42, Issue 3, Pages B761-B791Publisher
SIAM PUBLICATIONS
DOI: 10.1137/19M1261250
Keywords
poroelasticity; stable finite elements; block preconditioners; multigrid
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Funding
- National Science Foundation [DMS-1620063]
- NSF [DMS-1720114, DMS-1819157]
- Spanish project FEDER/MCYT [MTM2016-75139-R]
- Diputacion General de Aragon [E24 17R]
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In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [C. Rodrigo, X. Hu, P. Ohm, J. Adler, F. Gaspar, and L. Zikatanov, Comput. Methods Appl. Mech. Engrg., 341 (2018), pp. 467-484]. The discretization is proved to be well-posed with respect to the physical and discretization parameters and thus provides a framework to develop preconditioners that are robust with respect to such parameters as well. We construct both norm-equivalent (diagonal) and field-of-value-equivalent (triangular) preconditioners for both the stabilized discretization and a perturbation of the stabilized discretization, which leads to a smaller overall problem after static condensation. Numerical tests for both two- and three-dimensional problems confirm the robustness of the block preconditioners with respect to the physical and discretization parameters.
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