Discontinuous Galerkin Isogeometric Analysis on Non-matching Segmentation: Error Estimates and Efficient Solvers

TL;DR

This paper introduces discontinuous Galerkin isogeometric analysis techniques for elliptic problems on complex domains with non-matching patch interfaces, providing error estimates and efficient solvers for practical computations.

Contribution

It develops a novel dG IgA method for non-matching interfaces using Taylor expansions for flux approximation, along with domain decomposition solvers.

Findings

Numerical results validate theoretical error estimates.

The proposed method effectively handles non-matching patch interfaces.

Efficient solvers improve computational performance.

Abstract

The Isogeometric Analysis (IgA) of boundary value problems in complex domains often requires a decomposition of the computational domain into patches such that each of which can be parametrized by the so-called geometrical mapping. In this paper, we develop discontinuous Galerkin (dG) IgA techniques for solving elliptic diffusion problems on decompositions that can include non-matching parametrizations of the interfaces, i.e., the interfaces of the adjacent patches may be not identical. The lack of the exact parametrization of the patches leads to the creation of gap and overlapping regions between the patches. This does not allow the immediate use of the classical numerical fluxes that are known in the literature. The unknown normal fluxes of the solution on the non-matching interfaces are approximated by Taylor expansions using the values of the solution computed on the boundary of the patches These approximations are used in order to build up the numerical fluxes of the final dG IgA scheme and to couple the local patch-wise discrete problems. The resulting linear systems are solved by using efficient domainecomposition methods based on the tearing and interconnecting technology. We present numerical results of a series of test problems that validate the theoretical estimates presented.