Enhanced multiscale restriction-smoothed basis (MsRSB) preconditioning with applications to porous media flow and geomechanics

Sebastian B. M. Bosma, Sergey Klevtsov, Olav Møyner, Nicola Castelletto

Journal of Computational Physics


A novel multiscale method for non M-matrices using Multiscale Restricted Smoothed Basis (MsRSB) functions is presented. The original MsRSB method is enhanced with a filtering strategy enforcing M-matrix properties to enable the robust application of MsRSB as a preconditioner. Through applications to porous media flow and linear elastic geomechanics, the method is proven to be effective for scalar and vector problems with multipoint finite volume (FV) and finite element (FE) discretization schemes, respectively. Realistic complex (un)structured two- and three-dimensional test cases are considered to illustrate the method’s performance.

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MsRSB provides a flexible strategy to compute multiscale basis functions in realistic, unstructured settings. Here, we see several example basis functions for elasticity in a highly faulted reservoir.