Automatic conformal decomposition of elements cut by NURBS

In fictitious domain and extended finite element methods, elements cut by boundaries or interfaces are frequently present. They pose challenges with respect to the application of boundary and interface conditions, numerical integration, and the conditioning of the system of equations. A different path is the automatic decomposition of cut elements into smaller, conforming finite elements. Herein, we propose a concept for the automatic decomposition of elements cut by (curved) NURBS which automatically generates higher-order Lagrange elements on the two sides of the interfaces. The NURBS data, defining boundaries and interfaces in two dimensions, is converted into implicit level-set data by evaluating signed distance computations at all nodes in the background mesh. Based on the findings in [1] this data is then used for the decomposition into sub-elements. First numerical results are achieved as a proof-of-concept.