A novel block non-symmetric preconditioner for mixed-hybrid finite-element-based flow simulations

TL;DR

This paper introduces a new block preconditioner called EDFA that accelerates Krylov solver convergence for flow simulations in porous media, combining hybrid finite element and finite volume methods.

Contribution

The paper presents a novel EDFA preconditioner that leverages system matrix decoupling factors and adaptive restriction operators for improved flow simulation efficiency.

Findings

Demonstrates robustness across synthetic and real-case applications.

Achieves faster convergence of Krylov solvers.

Shows computational efficiency in large-scale simulations.

Abstract

In this work we propose a novel block preconditioner, labelled Explicit Decoupling Factor Approximation (EDFA), to accelerate the convergence of Krylov subspace solvers used to address the sequence of non-symmetric systems of linear equations originating from flow simulations in porous media. The flow model is discretized blending the Mixed Hybrid Finite Element (MHFE) method for Darcy's equation with the Finite Volume (FV) scheme for the mass conservation. The EDFA preconditioner is characterized by two features: the exploitation of the system matrix decoupling factors to recast the Schur complement and their inexact fully-parallel computation by means of restriction operators. We introduce two adaptive techniques aimed at building the restriction operators according to the properties of the system at hand. The proposed block preconditioner has been tested through an extensive experimentation on both synthetic and real-case applications, pointing out its robustness and computational efficiency.