A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics
Abstract
In this work, 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. 61856202; Comput. Methods Appl. Mech. Engrg., 300 (2016), pp. 129145]. A stable algorithm is advanced to compute the optimal value of $$\alpha$$, along with a lower bound to control the possible illconditioning of the $$\alpha$$ dependent inner blocks. Lastly, numerical experiments in both theoretical benchmarks and realworld applications are presented and discussed to investigate the RPF properties, performance, and robustness.
 Authors:

 Univ. of Padova (Italy)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1548353
 Report Number(s):
 LLNLJRNL756041
Journal ID: ISSN 10648275; 943354
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 41; Journal Issue: 4; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; preconditioning; Krylov subspace methods; mixed finite elements; poromechanics
Citation Formats
Frigo, Matteo, Castelletto, Nicola, and Ferronato, Massimiliano. A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics. United States: N. p., 2019.
Web. doi:10.1137/18M120645X.
Frigo, Matteo, Castelletto, Nicola, & Ferronato, Massimiliano. A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics. United States. doi:10.1137/18M120645X.
Frigo, Matteo, Castelletto, Nicola, and Ferronato, Massimiliano. Thu .
"A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics". United States. doi:10.1137/18M120645X. https://www.osti.gov/servlets/purl/1548353.
@article{osti_1548353,
title = {A Relaxed Physical Factorization Preconditioner for Mixed Finite Element Coupled Poromechanics},
author = {Frigo, Matteo and Castelletto, Nicola and Ferronato, Massimiliano},
abstractNote = {In this work, 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. 61856202; Comput. Methods Appl. Mech. Engrg., 300 (2016), pp. 129145]. A stable algorithm is advanced to compute the optimal value of $\alpha$, along with a lower bound to control the possible illconditioning of the $\alpha$ dependent inner blocks. Lastly, numerical experiments in both theoretical benchmarks and realworld applications are presented and discussed to investigate the RPF properties, performance, and robustness.},
doi = {10.1137/18M120645X},
journal = {SIAM Journal on Scientific Computing},
issn = {10648275},
number = 4,
volume = 41,
place = {United States},
year = {2019},
month = {7}
}
Web of Science