Analysis of discontinuous Galerkin dual-primal isogeometric tearing and interconnecting methods

TL;DR

This paper analyzes the dG-IETI-DP method, combining dual-primal isogeometric tearing with discontinuous Galerkin coupling, to handle non-matching grids and segmentation issues in 2D domain decomposition.

Contribution

It derives quasi-optimal condition number bounds for the method, considering non-matching grids and interface segmentation, with independence from mesh sizes.

Findings

Condition number bounds are independent of subdomain and mesh sizes.

The method effectively handles non-matching grids and segmentation crimes.

The analysis applies to 2D cases with vertex primal variables.

Abstract

In this paper, we present the analysis of the discontinuous Galerkin dual-primal isogeometric tearing and interconnecting method (dG-IETI-DP) for the two-dimensional case where we only consider vertex primal variables. The dG-IETI-DP method is a combination of the dual-primal isogeometric tearing and interconnecting method (IETI-DP) with the discontinuous Galerkin (dG) method. We use the dG method only on the interfaces to couple different patches. This enables us to handle non-matching grids on patch interfaces as well as segmentation crimes (gaps and overlaps) between the patches. The purpose of this paper is to derive quasi-optimal bounds for the condition number of the preconditioned system with respect to the maximal ratio $H/h:=\max_k(H_k/h_k)$ of subdomain diameter and meshsize. We show that the constant is independent of $h_k$ and $H_k$, but depends on the ratio of meshsizes of neighbouring patches $h_\ell/h_k$.