Abstract

In this paper, we introduce a relaxed physical factorization (RPF) preconditioner for the efficient iterative solution of the linearized algebraic system arising from the mixed finite element discretization of coupled poromechanics equations. The preconditioner is obtained by using a proper factorization of the $3\times3$ block matrix and setting a relaxation parameter $\alpha$. The preconditioner is inspired by the relaxed dimensional factorization introduced by Benzi et al. [J. Comput. Phys., 230 (2011), pp. 6185--6202; Comput. Methods Appl. Mech. Engrg., 300 (2016), pp. 129--145]. A stable algorithm is advanced to compute the optimal value of $\alpha$, along with a lower bound to control the possible ill-conditioning of the $\alpha$ dependent inner blocks. Numerical experiments in both theoretical benchmarks and real-world applications are presented and discussed to investigate the RPF properties, performance, and robustness.

Keywords

  1. preconditioning
  2. Krylov subspace methods
  3. mixed finite elements
  4. poromechanics

MSC codes

  1. 65F10
  2. 65F08
  3. 65N30

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: B694 - B720
ISSN (online): 1095-7197

History

Submitted: 9 August 2018
Accepted: 7 May 2019
Published online: 11 July 2019

Keywords

  1. preconditioning
  2. Krylov subspace methods
  3. mixed finite elements
  4. poromechanics

MSC codes

  1. 65F10
  2. 65F08
  3. 65N30

Authors

Affiliations

Funding Information

Lawrence Livermore National Laboratory https://doi.org/10.13039/100006227 : DE-AC52-07NA27344
Università degli Studi di Padova https://doi.org/10.13039/501100003500

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