Details
| Original language | English |
|---|---|
| Pages (from-to) | 1465-1502 |
| Number of pages | 38 |
| Journal | Computational Geosciences |
| Volume | 26 |
| Issue number | 6 |
| Early online date | 6 Aug 2022 |
| Publication status | Published - Dec 2022 |
Abstract
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.
Keywords
- Beavers-Joseph-Saffman conditions, Coupled Stokes/Darcy model, Discrete empirical interpolation method, In-situ leach mining, Model order reduction, Non-negativity preserving DEIM, Phase-field, Reduced basis method
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Earth and Planetary Sciences(all)
- Computers in Earth Sciences
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
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In: Computational Geosciences, Vol. 26, No. 6, 12.2022, p. 1465-1502.
Research output: Contribution to journal › Article › Research › peer review
}
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 -