A locally based construction of analysis-suitable $G^1$ multi-patch spline surfaces
Abstract
Analysis-suitable (AS-) multi-patch spline surfaces [4] are particular -smooth multi-patch spline surfaces, which are needed to ensure the construction of -smooth multi-patch spline spaces with optimal polynomial reproduction properties [16]. We present a novel local approach for the design of AS- multi-patch spline surfaces, which is based on the use of Lagrange multipliers. The presented method is simple and generates an AS- multi-patch spline surface by approximating a given -smooth but non-AS- multi-patch surface. Several numerical examples demonstrate the potential of the proposed technique for the construction of AS- multi-patch spline surfaces and show that these surfaces are especially suited for applications in isogeometric analysis by solving the biharmonic problem, a particular fourth order partial differential equation, with optimal rates of convergence over them.
Cite
@article{arxiv.2308.09007,
title = {A locally based construction of analysis-suitable $G^1$ multi-patch spline surfaces},
author = {Andrea Farahat and Mario Kapl and Aljaž Kosmač and Vito Vitrih},
journal= {arXiv preprint arXiv:2308.09007},
year = {2023}
}