Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Generating StarShaped Blocks for Scaled Boundary Multipatch IGA
 Brummelen, H. von: Isogeometric Analysis and Applications 2018 : Participants of the 3rd Conference on Isogeometric Analysis and Applications (IGAA 2018) held April 23rd26th, 2018 in Delft, The Netherlands Cham: Springer Nature, 2021 (Lecture notes in computational science and engineering 133) ISBN: 9783030498351 (Print) ISBN: 9783030498368 (Online) ISBN: 9783030498375 ISBN: 9783030498382 S.125 
 Conference on Isogeometric Analysis and Applications (IGAA) <3, 2018, Delft> 

 Englisch 
 Konferenzbeitrag 
 Fraunhofer ITWM () 
Abstract
This paper deals with the decomposition of a domain into starshaped blocks, which is motivated by the idea of solving PDEs by means of the scaled boundary isogeometric analysis (SBIGA). In the first part of the paper an introduction to the SBIGA is given and we show the necessity for the domain to be starshaped. Of course not every domain has this property, and for this reason the main focus of the paper is the generation of starshaped 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 starshapedness 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.