TY - JOUR

T1 - A DEIM driven reduced basis method for the diffuse Stokes/Darcy model coupled at parametric phase-field interfaces

AU - Stoter, Stein K. F.

AU - Jessen, Etienne

AU - Niedens, Viktor

AU - Schillinger, Dominik

N1 - Funding Information: Open Access funding enabled and organized by Projekt DEAL. The results presented in this paper were achieved as part of the ERC Starting Grant project “ImageToSim” that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 759001). The authors gratefully acknowledge this support.

PY - 2022/12

Y1 - 2022/12

N2 - In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal geometry. To accommodate possible changes in topology, we define the Stokes and Darcy domains implicitly via a phase-field indicator function. In our reduced order model, we approximate the parameter-dependent phase-field function with a discrete empirical interpolation method (DEIM) that enables affine decomposition of the associated linear and bilinear forms. In addition, we introduce a modification of DEIM that leads to non-negativity preserving approximations, thus guaranteeing positive-semidefiniteness of the system matrix. We also present a strategy for determining the required number of DEIM modes for a given number of reduced basis functions. We couple reduced basis functions on neighboring patches to enable the efficient simulation of large-scale problems that consist of repetitive subdomains. We apply our reduced basis framework to efficiently solve the inverse problem of characterizing the subsurface damage state of a complete in-situ leach mining site.

AB - In this article, we develop a reduced basis method for efficiently solving the coupled Stokes/Darcy equations with parametric internal geometry. To accommodate possible changes in topology, we define the Stokes and Darcy domains implicitly via a phase-field indicator function. In our reduced order model, we approximate the parameter-dependent phase-field function with a discrete empirical interpolation method (DEIM) that enables affine decomposition of the associated linear and bilinear forms. In addition, we introduce a modification of DEIM that leads to non-negativity preserving approximations, thus guaranteeing positive-semidefiniteness of the system matrix. We also present a strategy for determining the required number of DEIM modes for a given number of reduced basis functions. We couple reduced basis functions on neighboring patches to enable the efficient simulation of large-scale problems that consist of repetitive subdomains. We apply our reduced basis framework to efficiently solve the inverse problem of characterizing the subsurface damage state of a complete in-situ leach mining site.

KW - Beavers-Joseph-Saffman conditions

KW - Coupled Stokes/Darcy model

KW - Discrete empirical interpolation method

KW - In-situ leach mining

KW - Model order reduction

KW - Non-negativity preserving DEIM

KW - Phase-field

KW - Reduced basis method

UR - http://www.scopus.com/inward/record.url?scp=85135611187&partnerID=8YFLogxK

U2 - 10.1007/s10596-022-10164-4

DO - 10.1007/s10596-022-10164-4

M3 - Article

AN - SCOPUS:85135611187

VL - 26

SP - 1465

EP - 1502

JO - Computational Geosciences

JF - Computational Geosciences

SN - 1420-0597

IS - 6

ER -