Two-dimensional domain decomposition based on skeleton computation for parameterization and isogeometric analysis

Abstract

This paper proposes a method for decomposing two-dimensional domains into subdomains for parameterization and isogeometric analysis. Given a complex domain in a plane, the skeleton of the domain is computed to guide the domain decomposition. A continuous parameterization of the domain is then obtained by parameterizing each respective subdomain. This parameterization method is applied with isogeometric analysis to solve numerical PDEs over two-dimensional domains. Examples are provided to demonstrate that the new parameterization method is superior to other state-of-the-art parameterization techniques and that it performs better in isogeometric analysis.