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Computational Multiscale Methods for Linear Heterogeneous Poroelasticity

Computational Multiscale Methods for Linear Heterogeneous Poroelasticity
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Year:    2020

Author:    Robert Altmann, Eric T. Chung, Roland Maier, Daniel Peterseim, Sai-Mang Pun

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 41–57

Abstract

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough numerical treatment. In this paper, we propose a method based on the local orthogonal decomposition technique and motivated by a similar approach used for linear thermoelasticity. Therein, local corrector problems are constructed in line with the static equations, whereas we propose to consider the full system. This allows benefiting from the given saddle point structure and results in two decoupled corrector problems for the displacement and the pressure. We prove the optimal first-order convergence of this method and verify the result by numerical experiments.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1902-m2018-0186

Journal of Computational Mathematics, Vol. 38 (2020), Iss. 1 : pp. 41–57

Published online:    2020-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

Keywords:    Poroelasticity Heterogeneous media Numerical homogenization Multiscale methods.

Author Details

Robert Altmann

Eric T. Chung

Roland Maier

Daniel Peterseim

Sai-Mang Pun

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    Caiazzo, A. | Maier, R. | Peterseim, D.

    Journal of Scientific Computing, Vol. 85 (2020), Iss. 1

    https://doi.org/10.1007/s10915-020-01304-y [Citations: 5]

  2. Partially explicit generalized multiscale finite element methods for poroelasticity problem

    Su, Xin | Leung, Wing Tat | Li, Wenyuan | Pun, Sai-Mang

    Journal of Computational and Applied Mathematics, Vol. 448 (2024), Iss. P.115935

    https://doi.org/10.1016/j.cam.2024.115935 [Citations: 0]

  3. A Decoupling and Linearizing Discretization for Weakly Coupled Poroelasticity with Nonlinear Permeability

    Altmann, Robert | Maier, Roland

    SIAM Journal on Scientific Computing, Vol. 44 (2022), Iss. 3 P.B457

    https://doi.org/10.1137/21M1413985 [Citations: 5]

  4. Semi-explicit integration of second order for weakly coupled poroelasticity

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    BIT Numerical Mathematics, Vol. 64 (2024), Iss. 2

    https://doi.org/10.1007/s10543-024-01021-0 [Citations: 1]

  5. Numerical homogenization beyond scale separation

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    https://doi.org/10.1017/S0962492921000015 [Citations: 53]

  6. Port-Hamiltonian formulations of poroelastic network models

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    Mathematical and Computer Modelling of Dynamical Systems, Vol. 27 (2021), Iss. 1 P.429

    https://doi.org/10.1080/13873954.2021.1975137 [Citations: 16]

  7. A Multiscale Method for Heterogeneous Bulk-Surface Coupling

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    https://doi.org/10.1137/20M1338290 [Citations: 4]

  8. Multiscale methods for solving wave equations on spatial networks

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    https://doi.org/10.1016/j.cma.2023.116008 [Citations: 1]

  9. A semi‐explicit integration scheme for weakly‐coupled poroelasticity with nonlinear permeability

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    https://doi.org/10.1002/pamm.202000061 [Citations: 3]

  10. Fast online adaptive enrichment for poroelasticity with high contrast

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    Journal of Computational Physics, Vol. 487 (2023), Iss. P.112171

    https://doi.org/10.1016/j.jcp.2023.112171 [Citations: 2]

  11. Preconditioning Markov Chain Monte Carlo Method for Geomechanical Subsidence using multiscale method and machine learning technique

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    https://doi.org/10.1016/j.cam.2021.113420 [Citations: 18]

  12. A Priori Error Analysis of a Numerical Stochastic Homogenization Method

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    SIAM Journal on Numerical Analysis, Vol. 59 (2021), Iss. 2 P.660

    https://doi.org/10.1137/19M1308992 [Citations: 5]

  13. Fast Online Adaptive Enrichment for Poroelasticity with High Contrast

    Su, Xin | Pun, Sai-Mang

    SSRN Electronic Journal , Vol. (2022), Iss.

    https://doi.org/10.2139/ssrn.4196490 [Citations: 0]

  14. Regularized coupling multiscale method for thermomechanical coupled problems

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    Journal of Computational Physics, Vol. 499 (2024), Iss. P.112737

    https://doi.org/10.1016/j.jcp.2023.112737 [Citations: 1]

  15. Localized Orthogonal Decomposition for a Multiscale Parabolic Stochastic Partial Differential Equation

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    Multiscale Modeling & Simulation, Vol. 22 (2024), Iss. 1 P.204

    https://doi.org/10.1137/23M1569216 [Citations: 0]

  16. A Space-Time Multiscale Method for Parabolic Problems

    Ljung, Per | Maier, Roland | Målqvist, Axel

    Multiscale Modeling & Simulation, Vol. 20 (2022), Iss. 2 P.714

    https://doi.org/10.1137/21M1446605 [Citations: 5]