Rational approximation preconditioners for multiphysics problems

TL;DR

This paper introduces rational approximation preconditioners for multiphysics interface problems, demonstrating robustness and effectiveness in coupling Darcy and Stokes equations through fractional differential operators.

Contribution

It proposes a novel rational function approximation method for preconditioning fractional differential operators in multiphysics interface problems.

Findings

Robustness of approximation for fractional exponent functions

Effective preconditioning in Darcy-Stokes interface coupling

Potential for improved solver performance in multiphysics simulations

Abstract

We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of two fractional differential operators. We use a rational function approximation to precondition such operators. We first demonstrate the robustness of the approximation for ordinary functions given by weighted sums of fractional exponents. Additionally, we present more realistic examples utilizing the proposed preconditioning techniques in interface coupling between Darcy and Stokes equations.