Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 283, Issue -, Pages 841-855Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2014.09.023
Keywords
T-mesh; Spline space; Local refinement; Hierarchical B-splines
Funding
- Brain Korea 21 PLUS Project
- Industrial Strategic Technology Development Program of Ministry of Science, ICT & Future Planning [10047039]
- Basic Science Research Program through the National Research Foundation of Korea (NRF) - Ministry of Science, ICT & Future Planning [2012R1A1A1006109]
- National Research Foundation of Korea [2012R1A1A1006109] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
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In this paper we consider spaces of bivariate splines of bi-degree (m, n) with maximal order of smoothness over domains associated to a two-dimensional grid. We define admissible classes of domains for which suitable combinatorial technique allows us to obtain the dimension of such spline spaces and the number of tensor-product B-splines acting effectively on these domains. Following the strategy introduced recently by Giannelli and Juttler, these results enable us to prove that under certain assumptions about the configuration of a hierarchical T-mesh the hierarchical B-splines form a basis of bivariate splines of bi-degree (m, n) with maximal order of smoothness over this hierarchical T-mesh. In addition, we derive a sufficient condition about the configuration of a hierarchical T-mesh that ensures a weighted partition of unity property for hierarchical B-splines with only positive weights. (C) 2014 Elsevier B.V. All rights reserved.
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