Cn-continuous mortar method for Isogeometric Analysis

In recent years, isogeometric methods, using NURBS (Non-Uniform Rational B-Splines) as basis functions, have gained increasing attention. These methods offer exceptional flexibility in geometric modelling and the ability to adjust the smoothness of the piecewisedefined shape functions on a single patch as needed. This feature makes isogeometric analysis particularly attractive in the context of higher-order differential equations. However, to maintain this characteristic in the case of multiple patches, it must be appropriately accounted for in domain coupling.
This work addresses this challenge by presenting a novel method for implementing general non-conforming weak Cn-continuous domain couplings within the framework of isogeometric analysis. This approach builds upon the established mortar method and extends it by imposing additional constraints on derivatives up to a specified order. Within this study, the method is comprehensively elucidated using an abstract variational framework.
This encompasses discretisation within the context of isogeometric analysis, selection of the dual space, efficient handling of crosspoints and wirebaskets, and the evaluation of mortar integrals. A significant emphasis is also placed on the construction of isogeometric approximation spaces which a priori fulfil the higher-order coupling conditions.
Furthermore, the performance and applicability of the method are investigated in various engineering problems, including elasticity, heat conduction, diffusion and Phase-Field-Crystal modelling. This is achieved through a series of simulations that substantiate the applicability and efficiency of the approach in various technical domains.