Abstract
This work is dedicated to the computation of Euler Beta-function B-spline (BFBS) finite elements (FE) on triangulations, and to comparative visualization of their graphs. BFBS are a particular type of generalized expo-rational B-splines (GERBS) [2] and provide a piecewise polynomial modification of the true expo-rational B-splines (ERBS) [3]. The organization of the exposition is, as follows. First, we derive new formulae for triangular BFBS FE having C r smoothness at the vertices r ∈ ℕ. Second, we provide visualization of their graphs. Third, we compare the interpolatory and fitting properties of the new triangular BFBS FE of different polynomial degrees on two model surfaces used as a benchmark manifold.
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References
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Dechevsky, L.T., Zanaty, P. (2012). Triangular Beta-Function B-Spline Finite Elements: Evaluation and Graphical Comparisons. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_48
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DOI: https://doi.org/10.1007/978-3-642-29843-1_48
Publisher Name: Springer, Berlin, Heidelberg
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