Effective Preconditioners for Mixed-Dimensional Scalar Elliptic Problems

TL;DR

This paper introduces an efficient linear solver with a novel preconditioner for large mixed-dimensional scalar elliptic systems arising in fractured porous media, demonstrating robustness and effectiveness through numerical benchmarks.

Contribution

It presents a new preconditioning approach combining block factorization and algebraic multigrid for mixed-dimensional elliptic problems, improving solver performance.

Findings

Solver is robust across various physical parameters

Preconditioner accelerates convergence significantly

Effective on complex fracture structure benchmarks

Abstract

Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional scalar elliptic problems. We design an effective preconditioner based on approximate block factorization and algebraic multigrid techniques. Numerical results on benchmarks with complex fracture structures demonstrate the effectiveness of the proposed linear solver and its robustness with respect to different physical and discretization parameters.