Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry
For computational mechanics practitioners using spline-based isogeometric analysis, this method simplifies multi-patch coupling by enabling adaptive error control without extra DOFs.
This paper introduces the isogeometric Bézier dual mortar method, which enforces weak continuity at patch interfaces without additional degrees of freedom, and demonstrates its utility on challenging benchmarks.
In this paper we develop the isogeometric Bézier dual mortar method. It is based on Bézier extraction and projection and is applicable to any spline space which can be represented in Bézier form (i.e., NURBS, T-splines, LR-splines, etc.). The approach weakly enforces the continuity of the solution at patch interfaces and the error can be adaptively controlled by leveraging the refineability of the underlying dual spline basis without introducing any additional degrees of freedom. We also develop weakly continuous geometry as a particular application of isogeometric Bézier dual mortaring. Weakly continuous geometry is a geometry description where the weak continuity constraints are built into properly modified Bézier extraction operators. As a result, multi-patch models can be processed in a solver directly without having to employ a mortaring solution strategy. We demonstrate the utility of the approach on several challenging benchmark problems. Keywords: Mortar methods, Isogeometric analysis, Bézier extraction, Bézier projection