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

TL;DR

This paper introduces an enhanced MsRSB preconditioning method that incorporates a filtering strategy to extend its applicability to non-M-matrices, demonstrating effectiveness in porous media flow and geomechanics applications.

Contribution

The paper presents a novel filtering strategy that enables MsRSB to be applied to non-M-matrices, broadening its use in complex scalar and vector problems.

Findings

Effective in porous media flow simulations

Applicable to linear elastic geomechanics problems

Works with multipoint FV and FE discretizations

Abstract

A novel method to enable application of the Multiscale Restricted Smoothed Basis (MsRSB) method to non M-matrices 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.