Dual-Primal Isogeometric Tearing and Interconnecting solvers for multipatch dG-IgA equations

TL;DR

This paper introduces a new dual-primal IETI-DP method for efficiently solving large-scale dG-IgA equations on multipatch domains, demonstrating robustness and favorable condition number bounds.

Contribution

The paper presents a novel dual-primal IETI-DP solver tailored for multipatch dG-IgA problems, with theoretical analysis and numerical validation.

Findings

Polylogarithmic condition number bound for the preconditioned system

Robustness against large jumps in diffusion coefficients

Effective coupling of local problems across patch interfaces

Abstract

In this paper we consider a new version of the dual-primal isogeometric tearing and interconnecting (IETI-DP) method for solving large-scale linear systems of algebraic equations arising from discontinuous Galerkin (dG) isogeometric analysis of diffusion problems on multipatch domains with non-matching meshes. The dG formulation is used to couple the local problems across patch interfaces. The purpose of this paper is to present this new method and provide numerical examples indicating a polylogarithmic condition number bound for the preconditioned system and showing an incredible robustness with respect to large jumps in the diffusion coefficient across the interfaces.