Additive Average Schwarz Method for Elliptic Mortar Finite Element Problems with Highly Heterogeneous Coefficients

TL;DR

This paper develops an extended additive average Schwarz method for elliptic problems with highly heterogeneous coefficients, using mortar finite element discretization on nonmatching meshes, and proves its condition number is independent of coefficient jumps.

Contribution

It introduces a novel two-level additive Schwarz method with enriched coarse spaces based on eigenfunctions, improving robustness for heterogeneous coefficients.

Findings

Condition numbers are of order O(H/h)

Method is independent of coefficient jumps

Enriched coarse spaces enhance solver robustness

Abstract

In this paper, we extend the additive average Schwarz method to solve second order elliptic boundary value problems with heterogeneous coefficients inside the subdomains and across their interfaces by the mortar technique, where the mortar finite element discretization is on nonmatching meshes. In this two-level method, we enrich the coarse space in two different ways, i.e., by adding eigenfunctions of two variants of the generalized eigenvalue problems. We prove that the condition numbers of the systems of algebraic equations resulting from the extended additive average Schwarz method, corresponding to both coarse spaces, are of the order O(H/h) and independent of jumps in the coefficients, where H and h are the mesh parameters.