C^1 isogeometric spline space for trilinearly parameterized multi-patch volumes
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We study the space of C^1 isogeometric spline functions defined on trilinearly parameterized multi-patch volumes. Amongst others, we present a general framework for the design of the C^1 isogeometric spline space and of an associated basis, which is based on the two-patch construction [1], 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 C^1 isogeometric spline space and use the constructed C^1 isogeometric basis functions to numerically explore the approximation properties of the C^1 spline space by performing L^2 approximation.
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