Enhanced integration scheme for unfitted polygonal elements

Abstract

In this contribution a novel integration scheme, extending the conventional quadtree-decomposition-based approach by image compression techniques, is investigated for unfitted polygonal meshes with a particular focus on the rational Wachspress shape functions. It is shown that a meaningful reduction of integration points can be achieved without a significant loss in accuracy. However, the full potential of the method in terms of time savings can only be leveraged when applied to higher order polynomial elements. For more information on this topic see Enhanced Numerical Integration Scheme Based on Image Compression Techniques: Application to Rational Polygonal Interpolants by Petö et al. [1].