BDDC and FETI-DP for the Virtual Element Method

TL;DR

This paper develops and analyzes BDDC and FETI-DP preconditioners tailored for elliptic problems discretized with the virtual element method, providing theoretical bounds and numerical validation.

Contribution

It introduces and rigorously analyzes domain decomposition preconditioners specifically designed for VEM discretizations, with proven polylogarithmic condition number bounds.

Findings

Condition number bounds are polylogarithmic and independent of subdomain count.

Numerical experiments confirm the theoretical bounds.

Preconditioners are effective for elliptic problems discretized by VEM.

Abstract

We build and analyze Balancing Domain Decomposition by Constraint (BDDC) and Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioners for elliptic problems discretized by the virtual element method (VEM). We prove polylogarithmic condition number bounds, independent of the number of subdomains, the mesh size, and jumps in the diffusion coefficients. Numerical experiments confirm the theory.