Isogeometric multipatch coupling with arbitrary refinement and parametrization using the Gap–Shifted Boundary Method

Abstract

This work introduces a novel isogeometric multipatch coupling technique based on the Gap–Shifted Boundary Method (Gap–SBM). The method enables high-order, robust, and fully embedded coupling between nonconforming patches that may differ arbitrarily in element size, polynomial degree, orientation, and parametrization. In contrast to classical isogeometric multipatch strategies, the proposed approach avoids the need for watertight interfaces or matched knot vectors, and it preserves the conditioning of the discrete system by integrating over gap regions without introducing additional degrees of freedom. The coupling is enforced through a penalty-free Nitsche formulation. The framework also enables the insertion of locally refined subpatches around embedded boundaries, allowing h- and p-refinement to be introduced selectively while maintaining a consistent global discretization. A comprehensive set of numerical experiments demonstrates that the proposed multipatch coupling achieves both optimal convergence and favorable conditioning of the linear system, even in the presence of thin gap regions or highly nonconforming patches. The proposed methodology is assessed through numerical examples in two-dimensional settings.

The authors gratefully acknowledge the Design for IGA-type discretization workflows (GECKO) project. The Design for IGA-type discretization workflows has received funding from the European Union’s Horizon Europe research and Innovation programme under grant agreement No 101073106 Call: HORIZON-MSCA-2021-DN-01.

Peer Reviewed

Postprint (published version)