Approximate inverse-based block preconditioners in poroelasticity

We focus on the fully implicit solution of the linear systems arising from a three-field mixed finite element approximation of Biot's poroleasticity equations. The objective is to develop algebraic block preconditioners for the efficient solution of such systems by Krylov subspace methods. In this work, we investigate the use of approximate inverse-based techniques to decouple the native system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning of the unknowns by field type. The proposed methods are tested in various numerical experiments including real-world applications dealing with petroleum and geotechnical engineering.

Automated summary

The study focuses on developing algebraic block preconditioners for efficient solution of linear systems arising from a three-field mixed finite element approximation of Biot's poroelasticity equations. The proposed methods utilize approximate inverse-based techniques to decouple the original system of equations and obtain explicit sparse approximations of the Schur complements related to the physics-based partitioning. These methods have been tested in various numerical experiments, including applications in petroleum and geotechnical engineering.