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Standard and non-standard CAGD tools for isogeometric analysis: a tutorial. (English) Zbl 1356.65052

Buffa, Annalisa (ed.) et al., IsoGeometric analysis: a new paradigm in the numerical approximation of PDEs, Cetraro, Italy 2012. Based on lectures given at the summer school. Cham: Springer; Florence: Fondazione CIME (ISBN 978-3-319-42308-1/pbk; 978-3-319-42309-8/ebook). Lecture Notes in Mathematics 2161. CIME Foundation Subseries, 1-69 (2016).
Summary: We present a detailed summary of the main CAGD tools of interest in IgA: Bernstein polynomials and B-splines. Besides their well-known algebraic and geometric properties, we give a deeper insight into why these representations are so popular and efficient by proving that they are optimal bases for the corresponding function spaces. Moreover, we review some generalizations of the B-spline structure in function spaces which extend classical polynomial spaces. Extensions to the bivariate setting beyond the straightforward tensor-product case are discussed as well. In particular, we focus on the triangular setting.
For the entire collection see [Zbl 1355.65004].

MSC:

65D17 Computer-aided design (modeling of curves and surfaces)

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References:

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