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 address 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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This project has received funding from the The Research Council of Norway under grant agreement No 270922.
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Stangeby, I., Dokken, T. (2021). Properties of Spline Spaces Over Structured Hierarchical Box Partitions. In: van Brummelen, H., Vuik, C., Möller, M., Verhoosel, C., Simeon, B., Jüttler, B. (eds) Isogeometric Analysis and Applications 2018. IGAA 2018. Lecture Notes in Computational Science and Engineering, vol 133. Springer, Cham. https://doi.org/10.1007/978-3-030-49836-8_9
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DOI: https://doi.org/10.1007/978-3-030-49836-8_9
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