Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries

Nitsche’s method can be used as a coupling tool for non-matching discretizations by weakly enforcing interface constraints. We explore the use of weak coupling based on Nitsche’s method in the context of higher order and higher continuity B-splines and NURBS. We demonstrate that weakly coupled spline discretizations do not compromise the accuracy of isogeometric analysis. We show that the combination of weak coupling with the finite cell method opens the door for a truly isogeometric treatment of trimmed B-spline and NURBS geometries that eliminates the need for costly reparameterization procedures. We test our methodology for several relevant technical problems in two and three dimensions, such as gluing together trimmed multi-patches and connecting non-matching meshes that contain B-spline basis functions and standard triangular finite elements. The results demonstrate that the concept of Nitsche based weak coupling in conjunction with the finite cell method has the potential to considerably increase the flexibility of the design-through-analysis process in isogeometric analysis.