Planar multi-patch domain parameterization via patch adjacency graphs. (January 2017)

• Record Type: Journal Article
• Authors: Buchegger, Florian; Jüttler, Bert
• Is Part Of: Computer aided design. Volume 82(2017)
• Page Start: 2
• Page End: 12
• Publication Date: 2017-01
• Subjects: Parameterization -- Multi-patch domains -- Isogeometric analysis; Computer-aided design -- Periodicals; Engineering design -- Data processing -- Periodicals; Computer graphics -- Periodicals; Conception technique -- Informatique -- Périodiques; Infographie -- Périodiques; Computer graphics; Engineering design -- Data processing; Periodicals; Electronic journals; 620.00420285
• DOI: 10.1016/j.cad.2016.05.019
• Languages: English
• ISSNs: 0010-4485

Abstract

Abstract: As a remarkable difference to the existing CAD technology, where shapes are represented by their boundaries, FEM-based isogeometric analysis typically needs a parameterization of the interior of the domain. Due to the strong influence on the accuracy of the analysis, methods for constructing a good parameterization are fundamentally important. The flexibility of single patch representations is often insufficient, especially when more complex geometric shapes have to be represented. Using a multi-patch structure may help to overcome this challenge. In this paper we present a systematic method for exploring the different possible parameterizations of a planar domain by collections of quadrilateral patches. Given a domain, which is represented by a certain number of boundary curves, our aim is to find the optimal multi-patch parameterization with respect to an objective function that captures the parameterization quality. The optimization considers both the location of the control points and the layout of the multi-patch structure. The latter information is captured by pre-computed catalogs of all available multi-patch topologies. Several numerical examples demonstrate the performance of the method. Highlights: A method for finding a multi-patch parameterization for a domain is presented. The control points as well as the layout of the multi-patch structure are considered. Pre-computed catalogs of all available multi-patch topologies are used.