Discontinuous Galerkin Isogeometric Analysis for segmentations generating overlapping regions

TL;DR

This paper introduces a Discontinuous Galerkin Isogeometric Analysis method tailored for multipatch domains with small overlaps, providing theoretical error bounds and numerical validation for improved computational domain handling.

Contribution

The work develops a novel DG-IGA approach that effectively manages overlapping regions in multipatch geometries, with rigorous error analysis and practical verification.

Findings

The method accurately handles small overlaps in multipatch domains.

Theoretical error bounds are established and confirmed numerically.

Numerical examples demonstrate the method's effectiveness.

Abstract

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.