Scalable algorithms for three-field mixed finite element coupled poromechanics
Abstract
We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 x 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. In conclusion, the performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.
- Authors:
-
[3]
- Stanford Univ., CA (United States). Energy Resources Engineering
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
- Univ. of Padova (Italy). Dept. of Civil, Environmental and Architectural Engineering
- Publication Date:
- Research Org.:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1463016
- Alternate Identifier(s):
- OSTI ID: 1397767
- Report Number(s):
- LLNL-JRNL-737320
Journal ID: ISSN 0021-9991; 889967; TRN: US1902250
- Grant/Contract Number:
- AC52-07NA27344; AC52-07-NA27344
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 327; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Poromechanics; Preconditioners; Iterative methods; Mixed formulation; Algebraic multigrid
Citation Formats
Castelletto, Nicola, White, Joshua A., and Ferronato, Massimiliano. Scalable algorithms for three-field mixed finite element coupled poromechanics. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.09.063.
Castelletto, Nicola, White, Joshua A., & Ferronato, Massimiliano. Scalable algorithms for three-field mixed finite element coupled poromechanics. United States. https://doi.org/10.1016/j.jcp.2016.09.063
Castelletto, Nicola, White, Joshua A., and Ferronato, Massimiliano. Mon .
"Scalable algorithms for three-field mixed finite element coupled poromechanics". United States. https://doi.org/10.1016/j.jcp.2016.09.063. https://www.osti.gov/servlets/purl/1463016.
@article{osti_1463016,
title = {Scalable algorithms for three-field mixed finite element coupled poromechanics},
author = {Castelletto, Nicola and White, Joshua A. and Ferronato, Massimiliano},
abstractNote = {We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 x 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. In conclusion, the performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.},
doi = {10.1016/j.jcp.2016.09.063},
journal = {Journal of Computational Physics},
number = C,
volume = 327,
place = {United States},
year = {Mon Oct 03 00:00:00 EDT 2016},
month = {Mon Oct 03 00:00:00 EDT 2016}
}
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