Scalable algorithms for threefield 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 threefield formulation. The use of a displacement/velocity/pressure mixed finiteelement 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 twolevel Schur complement with the aid of physicallybased 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 realworld challenging consolidation experiment of a shallow formation.
 Authors:

 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 Lab. (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):
 LLNLJRNL737320
Journal ID: ISSN 00219991; 889967; TRN: US1902250
 Grant/Contract Number:
 AC5207NA27344; AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 327; Journal Issue: C; Journal ID: ISSN 00219991
 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 threefield 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 threefield mixed finite element coupled poromechanics. United States. doi:10.1016/j.jcp.2016.09.063.
Castelletto, Nicola, White, Joshua A., and Ferronato, Massimiliano. Mon .
"Scalable algorithms for threefield mixed finite element coupled poromechanics". United States. doi:10.1016/j.jcp.2016.09.063. https://www.osti.gov/servlets/purl/1463016.
@article{osti_1463016,
title = {Scalable algorithms for threefield 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 threefield formulation. The use of a displacement/velocity/pressure mixed finiteelement 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 twolevel Schur complement with the aid of physicallybased 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 realworld 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 = {2016},
month = {10}
}
Web of Science