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

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, define Stokes and Darcy domains implicitly via phase-field indicator function. our order model, approximate parameter-dependent function discrete empirical interpolation (DEIM) that enables affine decomposition of associated linear bilinear forms. addition, introduce modification DEIM leads to non-negativity preserving approximations, thus guaranteeing positive-semidefiniteness system matrix. We also present strategy determining required number modes given functions. couple functions on neighboring patches enable efficient simulation large-scale problems consist repetitive subdomains. apply framework solve inverse problem characterizing subsurface damage state complete in-situ leach mining site.