A FETI-DP preconditioner of discontinuous Galerkin method for multiscale problems in high constrast media

TL;DR

This paper introduces a FETI-DP preconditioner for discontinuous Galerkin discretizations of second order elliptic PDEs with highly heterogeneous coefficients, enabling efficient solutions in multiscale high contrast media.

Contribution

The paper develops and analyzes a novel FETI-DP preconditioner tailored for DG methods applied to multiscale problems with high contrast coefficients, without requiring matching grids.

Findings

Preconditioner improves convergence for high contrast media.

Numerical results validate theoretical performance.

Method handles nonmatching grids across subdomains.

Abstract

In this paper we consider second order elliptic partial differential equations with highly varying (heterogeneous) coefficients on a two-dimensional region. The problems are discretized by a composite finite element (FE) and discontinuous Galerkin (DG) Method. The fine grids are in general nonmatching across the subdomain boundaries, and the subdomain partitioning does not need to resolve the jumps in the coefficient. A FETI-DP preconditioner is proposed and analyzed to solve the resulting linear system. Numerical results are presented to support our theory.