Ioannis Toulopoulos

Multipatch Discontinuous Galerkin Isogeometric Analysis

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.

Analysis of multipatch discontinuous Galerkin IgA approximations to elliptic boundary value problems

In this work, we study the approximation properties of multipatch dG-IgA methods, that apply the multipatch Isogeometric Analysis discretization concept and the discontinuous Galerkin technique on the interfaces between the patches, for solving linear diffusion problems with diffusion coefficients that may be discontinuous across the patch interfaces. The computational domain is divided into non-overlapping subdomains, called patches in IgA, where B-splines, or NURBS approximations spaces are constructed. The solution of the problem is approximated in every subdomain without imposing any matching grid conditions and without any continuity requirements for the discrete solution across the interfaces. Numerical fluxes with interior penalty jump terms are applied in order to treat the discontinuities of the discrete solution on the interfaces. We provide a rigorous a priori discretization error analysis for diffusion problems in two- and three-dimensional domains, where solutions patchwise belong to

Mesh grading in isogeometric analysis

W^{l,p}

Space-time finite element methods stabilized using bubble function spaces

Wl,p, with some

Numerical Methods for Power-Law Diffusion Problems

l\ge 2

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

l≥2 and