FETI-DP preconditioners for the Virtual Element Method on general 2D meshes

TL;DR

This paper evaluates the FETI-DP domain decomposition method's scalability and robustness for solving large linear systems from elliptic problems discretized by the Virtual Element Method on complex 2D meshes.

Contribution

It demonstrates the effectiveness and robustness of FETI-DP for VEM discretizations on arbitrary meshes with heterogeneous coefficients, including highly irregular geometries.

Findings

FETI-DP is numerically scalable with problem size and subdomains.

The method is robust against coefficient jumps.

Performance remains stable on complex Voronoi meshes.

Abstract

We analyze the performance of a state-of-the-art domain decomposition approach, the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) method, for the efficient solution of very large linear systems arising from elliptic problems discretized by the Virtual Element Method. We provide numerical experiments on a model linear elliptic problem with highly heterogeneous diffusion coefficients on arbitrary Voronoi meshes, which we modify by adding nodes and edges deriving from the intersection with an unrelated coarse decomposition. The experiments confirm also in this case that the FETI-DP method is numerically scalable with respect to both the problem size and number of subdomains, and its performance is robust with respect to jumps in the diffusion coefficients and shape of the mesh elements.