Coupling non-conforming NURBS patches in isogeometric analysis using virtual refinement and a master-slave formulation

This work presents a simple yet robust method for coupling non-conforming NURBS patches in isogeometric frameworks. It consists of virtually refining bordering patches to derive coupling constraints in a master-slave formulation. These constraints are then enforced via a substitution method for condensation of the slave variables, thereby reducing the model size. The coupling relationships only depend on the mesh itself and not on any problem-dependent parameters, resulting in a natural coupling with a very low computational cost. In the special case of hierarchical meshes, the method results in an exact connection. For an arbitrary non-conforming configuration, however, the intrinsic mismatch between the interface basis functions prevents an exact coupling. In that case, the master-slave formulation takes the conflicting interface constraints into account naturally in a least-squares sense. This yields an accurate coupling without overconstraining the interface. Besides its low computational cost, the main merit of the proposed method lies in its simplicity and its robustness. It can be applied fully automatically, without any user interaction, and also gives good results for strongly non-conforming patch configurations. Moreover, it can be used to just connect interface variables, but also to obtain higher-order smoothness across patch boundaries. This is demonstrated for several problem types, requiring both C0- and C1-continuity. Benchmarking of the proposed approach against existing similar techniques illustrates its superior accuracy.status: publishe