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Title: Enhanced relaxed physical factorization preconditioner for coupled poromechanics

Abstract

The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form C^ = (C + βFFT), where C is a symmetric positive definite matrix, FFT a rank-deficient term, and β a real non-negative coefficient. The inversion of C^, performed in an inexact way, can become unstable for large values of β, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with C^. This strategy can prove useful in other problems as well where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix C^. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of C^. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Furthermore, effectiveness and robustness of the proposed algorithms are demonstratedmore » in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.« less

Authors:
 [1];  [2]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of Padova (Italy)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1841859
Report Number(s):
LLNL-JRNL-798397
Journal ID: ISSN 0898-1221; 1000384
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford); Journal Volume: 106; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Preconditioning; Krylov subspace methods; Poromechanics

Citation Formats

Frigo, Matteo, Castelletto, Nicola, and Ferronato, Massimiliano. Enhanced relaxed physical factorization preconditioner for coupled poromechanics. United States: N. p., 2021. Web. doi:10.1016/j.camwa.2021.11.015.
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Frigo, Matteo, Castelletto, Nicola, & Ferronato, Massimiliano. Enhanced relaxed physical factorization preconditioner for coupled poromechanics. United States. https://doi.org/10.1016/j.camwa.2021.11.015
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Frigo, Matteo, Castelletto, Nicola, and Ferronato, Massimiliano. Wed . "Enhanced relaxed physical factorization preconditioner for coupled poromechanics". United States. https://doi.org/10.1016/j.camwa.2021.11.015. https://www.osti.gov/servlets/purl/1841859.
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@article{osti_1841859,
title = {Enhanced relaxed physical factorization preconditioner for coupled poromechanics},
author = {Frigo, Matteo and Castelletto, Nicola and Ferronato, Massimiliano},
abstractNote = {The relaxed physical factorization (RPF) preconditioner is a recent algorithm allowing for the efficient and robust solution to the block linear systems arising from the three-field displacement-velocity-pressure formulation of coupled poromechanics. For its application, however, it is necessary to invert blocks with the algebraic form C^ = (C + βFFT), where C is a symmetric positive definite matrix, FFT a rank-deficient term, and β a real non-negative coefficient. The inversion of C^, performed in an inexact way, can become unstable for large values of β, as it usually occurs at some stages of a full poromechanical simulation. In this work, we propose a family of algebraic techniques to stabilize the inexact solve with C^. This strategy can prove useful in other problems as well where such an issue might arise, such as augmented Lagrangian preconditioning techniques for Navier-Stokes or incompressible elasticity. First, we introduce an iterative scheme obtained by a natural splitting of matrix C^. Second, we develop a technique based on the use of a proper projection operator annihilating the near-kernel modes of C^. Both approaches give rise to a novel class of preconditioners denoted as Enhanced RPF (ERPF). Furthermore, effectiveness and robustness of the proposed algorithms are demonstrated in both theoretical benchmarks and real-world large-size applications, outperforming the native RPF preconditioner.},
doi = {10.1016/j.camwa.2021.11.015},
journal = {Computers and Mathematics with Applications (Oxford)},
number = ,
volume = 106,
place = {United States},
year = {Wed Dec 15 00:00:00 EST 2021},
month = {Wed Dec 15 00:00:00 EST 2021}
}
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