English

Robust preconditioners for a new stabilized discretization of the poroelastic equations

Numerical Analysis 2020-01-07 v2 Numerical Analysis

Abstract

In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [45]. 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 that 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.

Keywords

Cite

@article{arxiv.1905.10353,
  title  = {Robust preconditioners for a new stabilized discretization of the poroelastic equations},
  author = {James H. Adler and Francisco J. Gaspar and Xiaozhe Hu and Peter Ohm and Carmen Rodrigo and Ludmil T. Zikatanov},
  journal= {arXiv preprint arXiv:1905.10353},
  year   = {2020}
}