Domain decomposition solvers for operators with fractional interface perturbations

TL;DR

This paper introduces scalable, robust domain decomposition algorithms for operators with fractional interface perturbations, enhancing the efficiency of multiphysics solvers in strongly perturbed systems.

Contribution

It develops parameter-robust algorithms using fractional powers of the interfacial Laplacian as preconditioners, with rational approximation implementation.

Findings

Algorithms demonstrate scalability and robustness in numerical tests.

Preconditioners effectively handle strong fractional perturbations.

Application to Darcy-Stokes problem confirms practical efficiency.

Abstract

Operators with fractional perturbations are crucial components for robust preconditioning of interface-coupled multiphysics systems. However, in case the perturbation is strong, standard approaches can fail to provide scalable approximation of the inverse, thus compromising efficiency of the entire multiphysics solver. In this work, we develop efficient and parameter-robust algorithms for interface-perturbed operators based on the non-overlapping domain decomposition method. As preconditioners for the resulting Schur complement problems we utilize (inverses of) weighted sums of fractional powers of the interfacial Laplacian. Realization of the preconditioner in terms of rational approximation is discussed. We demonstrate performance of the solvers by numerical examples including application to coupled Darcy-Stokes problem.