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09.08.2024 | Original Article

Spectrum analysis of \(C^0\), \(C^1\), and \(G^1\) constructions for extraordinary points

verfasst von: Md Sadman Faruque, Zuowei Wen, Xiaodong Wei, Hugo Casquero

Erschienen in: Engineering with Computers | Ausgabe 6/2024

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Abstract

G-splines are smooth spline surface representations that support control nets with arbitrary unstructured quadrilateral layout. Supporting any distribution of extraordinary points (EPs) is necessary to satisfactorily meet the demands of real-world engineering applications. G-splines impose \(G^1\) constraints across the edges emanating from the EPs, which leads to discretizations with global \(C^1\) continuity in physical space when used in isogeometric analysis (IGA). In this work, we perform spectrum analyses of G-splines for the first time. Our results suggest that G-splines do not have outliers near the boundary when uniform elements and control nets are used. When EPs are considered, G-splines result in significantly higher spectral accuracy than the D-patch framework. In addition, we develop G-spline discretizations that use bi-quartic elements around EPs instead of bi-quintic elements around EPs as it was the case in our preceding work. All the other elements are bi-cubic. Our evaluations of surface quality, convergence studies of linear elliptic boundary-value problems, and spectral analyses suggest that using bi-quartic elements around EPs is preferable for IGA since they result in similar performance as using bi-quintic elements around EPs while being more computationally efficient.

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Fußnoten
1
We solved this problem with other exact solutions (including polynomials and exponential functions) and found out that the accuracy of G-splines was also superior to the D-patch framework for coarse and intermediate mesh resolutions, but we are evidently not claiming this to always be the case.
 
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Metadaten
Titel
Spectrum analysis of , , and constructions for extraordinary points
verfasst von
Md Sadman Faruque
Zuowei Wen
Xiaodong Wei
Hugo Casquero
Publikationsdatum
09.08.2024
Verlag
Springer London
Erschienen in
Engineering with Computers / Ausgabe 6/2024
Print ISSN: 0177-0667
Elektronische ISSN: 1435-5663
DOI
https://doi.org/10.1007/s00366-024-02012-z