Generalized B-Splines in Isogeometric Analysis

In this paper, we survey the use of generalized B-splines in isogeometric Galerkin and collocation methods. Generalized B-splines are a special class of Tchebycheffian B-splines and form an attractive alternative to standard polynomial B-splines and NURBS in both modeling and simulation. We summarize their definition and main properties, and we illustrate their use in a selection of numerical examples in the context of isogeometric analysis. For practical applications, we mainly focus on trigonometric and hyperbolic generalized B-splines.

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