Robust preconditioners for a new stabilized discretization of the poroelastic equations.
SIAM JOURNAL ON SCIENTIFIC COMPUTING(2020)
Abstract
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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Key words
poroelasticity,stable finite elements,block preconditioners,multigrid
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