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Title: Block preconditioning for fault/fracture mechanics saddle-point problems

Abstract

The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddle-point structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov methods for such problems. We critically review possible advantages and difficulties of using various Schur complement approximations, based on both physical and algebraic considerations. In conclusion, the proposed approaches are tested in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned problems.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [1]
  1. Univ. of Padova, Padua (Italy)
  2. Stanford Univ., CA (United States); 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:
1548375
Report Number(s):
LLNL-JRNL-746123
Journal ID: ISSN 0045-7825; 930434
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 344; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
Engineering - Mechanical and civil engineering, Geosciences, Mathematics and Computing; Fault mechanics; Lagrange multipliers; Preconditioners; Saddle point problems; Iterative methods

Citation Formats

Franceschini, Andrea, Castelletto, Nicola, and Ferronato, Massimiliano. Block preconditioning for fault/fracture mechanics saddle-point problems. United States: N. p., 2018. Web. doi:10.1016/j.cma.2018.09.039.
Franceschini, Andrea, Castelletto, Nicola, & Ferronato, Massimiliano. Block preconditioning for fault/fracture mechanics saddle-point problems. United States. doi:10.1016/j.cma.2018.09.039.
Franceschini, Andrea, Castelletto, Nicola, and Ferronato, Massimiliano. Thu . "Block preconditioning for fault/fracture mechanics saddle-point problems". United States. doi:10.1016/j.cma.2018.09.039. https://www.osti.gov/servlets/purl/1548375.
@article{osti_1548375,
title = {Block preconditioning for fault/fracture mechanics saddle-point problems},
author = {Franceschini, Andrea and Castelletto, Nicola and Ferronato, Massimiliano},
abstractNote = {The efficient simulation of fault and fracture mechanics is a key issue in several applications and is attracting a growing interest by the scientific community. Using a formulation based on Lagrange multipliers, the Jacobian matrix resulting from the Finite Element discretization of the governing equations has a non-symmetric generalized saddle-point structure. In this work, we propose a family of block preconditioners to accelerate the convergence of Krylov methods for such problems. We critically review possible advantages and difficulties of using various Schur complement approximations, based on both physical and algebraic considerations. In conclusion, the proposed approaches are tested in a number of real-world applications, showing their robustness and efficiency also in large-size and ill-conditioned problems.},
doi = {10.1016/j.cma.2018.09.039},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 344,
place = {United States},
year = {2018},
month = {10}
}

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