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:
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (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; S0045782516000104; PII: S0045782516000104
- Grant/Contract Number:
- AC52-07NA27344
- Resource Type:
- Published Article
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Volume: 303 Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- Netherlands
- 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. Netherlands: 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. Netherlands. https://doi.org/10.1016/j.cma.2016.01.008
White, Joshua A., Castelletto, Nicola, and Tchelepi, Hamdi A. Sun .
"Block-partitioned solvers for coupled poromechanics: A unified framework". Netherlands. https://doi.org/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 = {Netherlands},
year = {Sun May 01 00:00:00 EDT 2016},
month = {Sun May 01 00:00:00 EDT 2016}
}
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https://doi.org/10.1016/j.cma.2016.01.008
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