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:
-
[2]
- Stanford Univ., CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
- Stanford Univ., CA (United States)
- 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. https://doi.org/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. https://doi.org/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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Works referencing / citing this record:
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