Generating star-shaped blocks for scaled boundary multipatch IGA (Q1979740)

This article discusses numerical approximation methods for partial differential equations by means of the scaled boundary isogeometric analysis method. In the curent framework, the authors use the decomposition of a domain into star-shaped blocks, specifically named the quadtree decomposition and the art gallery decomposition. A computational criterion for the identification of the star-shapedness of a block is provided. In the case of the art gallery decomposition an extension of Fisk's method and the Voronoi diagram are employed. Applications to the Poisson equation on different geometries are included. For the entire collection see [Zbl 1467.65001].