Isogeometric B\'ezier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry

TL;DR

This paper introduces an isogeometric Bézier dual mortar method that enforces weak continuity across patches using Bézier extraction and projection, allowing adaptive refinement without extra degrees of freedom, and develops weakly continuous geometry for seamless multi-patch modeling.

Contribution

It presents a novel, refineable dual spline basis for isogeometric analysis and introduces weakly continuous geometry for integrated multi-patch models.

Findings

Effective weak enforcement of patch interface continuity.

Adaptive error control without additional degrees of freedom.

Demonstrated on challenging benchmark problems.

Abstract

In this paper we develop the isogeometric B\'ezier dual mortar method. It is based on B\'ezier extraction and projection and is applicable to any spline space which can be represented in B\'ezier 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 B\'ezier dual mortaring. Weakly continuous geometry is a geometry description where the weak continuity constraints are built into properly modified B\'ezier 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, B\'ezier extraction, B\'ezier projection