Properties of Spline Spaces Over Structured Hierarchical Box Partitions

Ivar Stangeby; Tor Dokken

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arXiv · 1906.03061

Properties of Spline Spaces Over Structured Hierarchical Box Partitions

Ivar Stangeby·Tor Dokken

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Abstract

Given a spline space spanned by Truncated Hierarchical B-splines (THB), it is always possible to construct a spline space spanned by Locally Refined B-splines (LRB) that contains the THB-space. Starting from configurations where the two spline spaces are equal, we adress what happens to the properties of the LRB-space when it is modified by local one-directional refinement at convex corners of, and along edges between dyadic refinement regions. We show that such local modifications can reduce the number of B-splines over each element to the minimum prescribed by the polynomial bi-degree, and that such local refinements can be used for improving the condition numbers of mass and stiffness matrices.

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Ivar Stangeby, Tor Dokken. 2019-06-07. Properties of Spline Spaces Over Structured Hierarchical Box Partitions. https://arxiv.org/abs/1906.03061

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