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$C^1$ isogeometric spline space for trilinearly parameterized multi-patch volumes

Numerical Analysis 2021-10-06 v2 Numerical Analysis

Abstract

We study the space of C1C^1 isogeometric spline functions defined on trilinearly parameterized multi-patch volumes. Amongst others, we present a general framework for the design of the C1C^1 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 C1C^1 isogeometric spline space and use the constructed C1C^1 isogeometric basis functions to numerically explore the approximation properties of the C1C^1 spline space by performing L2L^2 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}
}
R2 v1 2026-06-23T21:42:06.037Z