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Title: Scalable algorithms for three-field mixed finite element coupled poromechanics

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.
 [1] ;  [2] ; ORCiD logo [3]
  1. Stanford Univ., CA (United States). Energy Resources Engineering
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division
  3. Univ. of Padova (Italy). Dept. of Civil, Environmental and Architectural Engineering
Publication Date:
Report Number(s):
Journal ID: ISSN 0021-9991; 889967
Grant/Contract Number:
AC52-07NA27344; AC52-07-NA27344
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 327; Journal Issue: C; Journal ID: ISSN 0021-9991
Research Org:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org:
USDOE National Nuclear Security Administration (NNSA)
Country of Publication:
United States
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Poromechanics; Preconditioners; Iterative methods; Mixed formulation; Algebraic multigrid
OSTI Identifier:
Alternate Identifier(s):
OSTI ID: 1397767