h-Refinement method for toric parameterization of planar multi-sided computational domain in isogeometric analysis

Ji, Yindong; Li, Jinggai; Zhu, Chun‐Gang

doi:10.1016/j.cagd.2022.102065

Cited by 7 publications

(1 citation statement)

References 47 publications

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“…Bézier and B-spline surfaces) to parametrize multi-sided domains may cause mesh degeneration or decreased continuity. As far as we know, only a few papers discuss the polygonal toric surface techniques in the parameterization for IGA [12,18]. However, this method is sometimes unsatisfactory in terms of the quality of the parameterization.…”

Section: Introductionmentioning

confidence: 99%

Degree Elevation and Knot Insertion for Generalized Bézier Surfaces and Their Application to Isogeometric Analysis

Mengyun Wang,

Ye Ji,

Chungang Zhu

2024

JCM

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Generalized Bézier surfaces are a multi-sided generalization of classical tensor product Bézier surfaces with a simple control structure and inherit most of the appealing properties from Bézier surfaces. However, the original degree elevation changes the geometry of generalized Bézier surfaces such that it is undesirable in many applications, e.g. isogeometric analysis. In this paper, we propose an improved degree elevation algorithm for generalized Bézier surfaces preserving not only geometric consistency but also parametric consistency. Based on the knot insertion of B-splines, a novel knot insertion algorithm for generalized Bézier surfaces is also proposed. Then the proposed algorithms are employed to increase degrees of freedom for multi-sided computational domains parameterized by generalized Bézier surfaces in isogeometric analysis, corresponding to the traditional p-, h-, and k-refinements. Numerical examples demonstrate the effectiveness and superiority of our method.

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Section: Introductionmentioning

confidence: 99%