Discontinuous Galerkin Isogeometric Analysis for segmentations generating overlapping regions
It addresses the practical problem of handling overlapping patch interfaces in CAD-derived IGA models, but the approach is incremental and domain-specific.
The paper develops a Discontinuous Galerkin Isogeometric Analysis method for multipatch domains with small overlapping regions, providing theoretical error bounds and numerical verification.
In the Isogeometric Analysis (IGA) framework, the computational domain has very often a multipatch representation. The multipatch domain can be obtained by a volume segmentation of a boundary represented domain, e.g., provided by a Computer Aided Design (CAD) model. Typically, small gap and overlapping regions can appear at the patch interfaces of such multipatch representations. In the current work we consider multipatch representations having only small overlapping regions between the patches. We develop a Discontinuous Galerkin (DG)- IGA method which can be immediately applied to these representations. Our method appropriately connects the fluxes of the one face of the overlapping region with the flux of the opposite face. We provide a theoretical justification of our approach by splitting the whole error into two components: the first is related to the incorrect representation of the patches (consistency error) and the second to the approximation properties of the IGA space. We show bounds for both components of the error. We verify the theoretical error estimates in a series of numerical examples.