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Title: Block-partitioned solvers for coupled poromechanics: A unified framework

Abstract

Here, coupled poromechanical problems appear in a variety of disciplines, from reservoir engineering to biomedical applications. This work focuses on efficient strategies for solving the matrix systems that result from discretization and linearization of the governing equations. These systems have an inherent block structure due to the coupled nature of the mass and momentum balance equations. Recently, several iterative solution schemes have been proposed that exhibit stable and rapid convergence to the coupled solution. These schemes appear distinct, but a unifying feature is that they exploit the block-partitioned nature of the problem to accelerate convergence. This paper analyzes several of these schemes and highlights the fundamental connections that underlie their effectiveness. We begin by focusing on two specific methods: a fully-implicit and a sequential-implicit scheme. In the first approach, the system matrix is treated monolithically, and a Krylov iteration is used to update pressure and displacement unknowns simultaneously.

Authors:
 [1];  [2];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Stanford Univ., Stanford, 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:
1302507
Alternate Identifier(s):
OSTI ID: 1474372
Report Number(s):
LLNL-JRNL-681067
Journal ID: ISSN 0045-7825; 805371
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Published Article
Journal Name:
Computer Methods in Applied Mechanics and Engineering
Additional Journal Information:
Journal Volume: 303; Journal Issue: C; Journal ID: ISSN 0045-7825
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 36 MATERIALS SCIENCE; Poromechanics; Iterative methods; Preconditioning; Algebraic multigrid; Fixed-stress split

Citation Formats

White, Joshua A., Castelletto, Nicola, and Tchelepi, Hamdi A. Block-partitioned solvers for coupled poromechanics: A unified framework. United States: N. p., 2016. Web. doi:10.1016/j.cma.2016.01.008.
White, Joshua A., Castelletto, Nicola, & Tchelepi, Hamdi A. Block-partitioned solvers for coupled poromechanics: A unified framework. United States. doi:10.1016/j.cma.2016.01.008.
White, Joshua A., Castelletto, Nicola, and Tchelepi, Hamdi A. Thu . "Block-partitioned solvers for coupled poromechanics: A unified framework". United States. doi:10.1016/j.cma.2016.01.008.
@article{osti_1302507,
title = {Block-partitioned solvers for coupled poromechanics: A unified framework},
author = {White, Joshua A. and Castelletto, Nicola and Tchelepi, Hamdi A.},
abstractNote = {Here, coupled poromechanical problems appear in a variety of disciplines, from reservoir engineering to biomedical applications. This work focuses on efficient strategies for solving the matrix systems that result from discretization and linearization of the governing equations. These systems have an inherent block structure due to the coupled nature of the mass and momentum balance equations. Recently, several iterative solution schemes have been proposed that exhibit stable and rapid convergence to the coupled solution. These schemes appear distinct, but a unifying feature is that they exploit the block-partitioned nature of the problem to accelerate convergence. This paper analyzes several of these schemes and highlights the fundamental connections that underlie their effectiveness. We begin by focusing on two specific methods: a fully-implicit and a sequential-implicit scheme. In the first approach, the system matrix is treated monolithically, and a Krylov iteration is used to update pressure and displacement unknowns simultaneously.},
doi = {10.1016/j.cma.2016.01.008},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 303,
place = {United States},
year = {2016},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1016/j.cma.2016.01.008

Citation Metrics:
Cited by: 13 works
Citation information provided by
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