$C^1$ isogeometric spline space for trilinearly parameterized multi-patch volumes
Abstract
We study the space of isogeometric spline functions defined on trilinearly parameterized multi-patch volumes. Amongst others, we present a general framework for the design of the isogeometric spline space and of an associated basis, which is based on the two-patch construction [7], and which works uniformly for any possible multi-patch configuration. The presented method is demonstrated in more detail on the basis of a particular subclass of trilinear multi-patch volumes, namely for the class of trilinearly parameterized multi-patch volumes with exactly one inner edge. For this specific subclass of trivariate multi-patch parameterizations, we further numerically compute the dimension of the resulting isogeometric spline space and use the constructed isogeometric basis functions to numerically explore the approximation properties of the spline space by performing approximation.
Keywords
Cite
@article{arxiv.2101.00404,
title = {$C^1$ isogeometric spline space for trilinearly parameterized multi-patch volumes},
author = {Mario Kapl and Vito Vitrih},
journal= {arXiv preprint arXiv:2101.00404},
year = {2021}
}