Multipatch discontinuous galerkin isogeometric analysis

Abstract

Isogeometric Analysis (IgA) uses the same class of basis functions for both representing the geometry of the computational domain and approximating the solution of the boundary value problem under consideration. 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 subdomains. The construction and the corresponding discretization error analysis of such dG multi-patch IgA schemes is 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.