Multipatch Discontinuous Galerkin Isogeometric Analysis

TL;DR

This paper introduces a discontinuous Galerkin isogeometric analysis method for multi-patch geometries, providing theoretical error analysis and numerical validation for heterogeneous diffusion problems in 2D and 3D domains.

Contribution

It develops a novel dG IgA framework for multi-patch geometries, including error analysis and implementation details for complex domains.

Findings

The method achieves accurate solutions for heterogeneous diffusion problems.

Numerical experiments confirm the theoretical error estimates.

The G+SMO library supports the implementation of the proposed methods.

Abstract

Isogeometric analysis (IgA) uses the same class of basis functions for both, representing the geometry of the computational domain and approximating the solution. In practical applications, geometrical patches are used in order to get flexibility in the geometrical representation. This multi-patch representation corresponds to a decomposition of the computational domain into non-overlapping subdomains also called patches in the geometrical framework. We will present discontinuous Galerkin (dG) methods that allow for discontinuities across the subdomain (patch) boundaries. The required interface conditions are weakly imposed by the dG terms associated with the boundary of the sub-domains. The construction and the corresponding discretization error analysis of such dG multi-patch IgA schemes will be given for heterogeneous diffusion model problems in volumetric 2d and 3d domains as well as on open and closed surfaces. The theoretical results are confirmed by numerous numerical experiments which have been performed in G+SMO. The concept and the main features of the IgA library G+SMO are also described.