Generating Star-Shaped Blocks for Scaled Boundary Multipatch IGA

This paper deals with the decomposition of a domain into star-shaped blocks, which is motivated by the idea of solving PDEs by means of the scaled boundary isogeometric analysis (SB-IGA). In the first part of the paper an introduction to the SB-IGA is given and we show the necessity for the domain to be star-shaped. Of course not every domain has this property, and for this reason the main focus of the paper is the generation of star-shaped blocks. The approaches that we take into account are the quadtree decomposition and the art gallery decomposition. We highlight the steps of those algorithms and we provide a computable sufficient criterion for the identification of the star-shapedness of a block. Moreover, for the art gallery decomposition an extension of Fisk’s method and the Voronoi diagram are employed. Finally we solve the Poisson equation on different geometries, among them the Yeti footprint domain, and compare the approaches.