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The Isogeometric Analysis (IgA) of boundary value problems in complex domainsoften requires a decomposition of the computational domain into patches suchthat each of which can be parametrized by the so-called geometrical mapping. Inthis paper, we develop discontinuous Galerkin (dG) IgA techniques for solvingelliptic diffusion problems on decompositions that can include non-matchingparametrizations of the interfaces, i.e., the interfaces of the adjacentpatches may be not identical. The lack of the exact parametrization of thepatches leads to the creation of gap and overlapping regions between thepatches. This does not allow the immediate use of the classical numericalfluxes that are known in the literature. The unknown normal fluxes of thesolution on the non-matching interfaces are approximated by Taylor expansionsusing the values of the solution computed on the boundary of the patches Theseapproximations are used in order to build up the numerical fluxes of the finaldG IgA scheme and to couple the local patch-wise discrete problems. Theresulting linear systems are solved by using efficient domainecompositionmethods based on the tearing and interconnecting technology. We presentnumerical results of a series of test problems that validate the theoreticalestimates presented.

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