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Title: Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media

Abstract

In this paper, we propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Lastly, various numerical experiments are used to demonstrate the robustness of the proposed solver.

Authors:
 [1];  [2];  [3]; ORCiD logo [2]
  1. Stanford Univ., CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Stanford Univ., CA (United States)
  3. Delft Univ. of Technology (Netherlands)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1548341
Report Number(s):
LLNL-JRNL-747875
Journal ID: ISSN 1420-0597; 932724
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Computational Geosciences
Additional Journal Information:
Journal Volume: 23; Journal Issue: 2; Journal ID: ISSN 1420-0597
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 97 MATHEMATICS AND COMPUTING; Poromechanics; Multiscale methods; Preconditioners; Iterative methods

Citation Formats

Castelletto, Nicola, Klevtsov, Sergey, Hajibeygi, Hadi, and Tchelepi, Hamdi A. Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media. United States: N. p., 2018. Web. doi:10.1007/s10596-018-9791-z.
Castelletto, Nicola, Klevtsov, Sergey, Hajibeygi, Hadi, & Tchelepi, Hamdi A. Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media. United States. doi:10.1007/s10596-018-9791-z.
Castelletto, Nicola, Klevtsov, Sergey, Hajibeygi, Hadi, and Tchelepi, Hamdi A. Fri . "Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media". United States. doi:10.1007/s10596-018-9791-z. https://www.osti.gov/servlets/purl/1548341.
@article{osti_1548341,
title = {Multiscale two-stage solver for Biot’s poroelasticity equations in subsurface media},
author = {Castelletto, Nicola and Klevtsov, Sergey and Hajibeygi, Hadi and Tchelepi, Hamdi A.},
abstractNote = {In this paper, we propose a two-stage preconditioner for accelerating the iterative solution by a Krylov subspace method of Biot’s poroelasticity equations based on a displacement-pressure formulation. The spatial discretization combines a finite element method for mechanics and a finite volume approach for flow. The fully implicit backward Euler scheme is used for time integration. The result is a 2 × 2 block linear system for each timestep. The preconditioning operator is obtained by applying a two-stage scheme. The first stage is a global preconditioner that employs multiscale basis functions to construct coarse-scale coupled systems using a Galerkin projection. This global stage is effective at damping low-frequency error modes associated with long-range coupling of the unknowns. The second stage is a local block-triangular smoothing preconditioner, which is aimed at high-frequency error modes associated with short-range coupling of the variables. Lastly, various numerical experiments are used to demonstrate the robustness of the proposed solver.},
doi = {10.1007/s10596-018-9791-z},
journal = {Computational Geosciences},
number = 2,
volume = 23,
place = {United States},
year = {2018},
month = {11}
}

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