Details
| Original language | English |
|---|---|
| Article number | 114115 |
| Pages (from-to) | 4023-4041 |
| Number of pages | 19 |
| Journal | Engineering with computers |
| Volume | 40 |
| Issue number | 6 |
| Early online date | 9 Aug 2024 |
| Publication status | Published - Dec 2024 |
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 G1 constraints across the edges emanating from the EPs, which leads to discretizations with global C1 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.
Keywords
- Eigenvalue problems, Extraordinary points, G-splines, Isogeometric analysis, Unstructured splines
ASJC Scopus subject areas
- Computer Science(all)
- Software
- Mathematics(all)
- Modelling and Simulation
- Engineering(all)
- General Engineering
- Computer Science(all)
- Computer Science Applications
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In: Engineering with computers, Vol. 40, No. 6, 114115, 12.2024, p. 4023-4041.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Spectrum analysis of C0, C1, and G1 constructions for extraordinary points
AU - Faruque, Md Sadman
AU - Wen, Zuowei
AU - Wei, Xiaodong
AU - Casquero, Hugo
N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature 2024.
PY - 2024/12
Y1 - 2024/12
N2 - 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 G1 constraints across the edges emanating from the EPs, which leads to discretizations with global C1 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.
AB - 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 G1 constraints across the edges emanating from the EPs, which leads to discretizations with global C1 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.
KW - Eigenvalue problems
KW - Extraordinary points
KW - G-splines
KW - Isogeometric analysis
KW - Unstructured splines
UR - http://www.scopus.com/inward/record.url?scp=85200997884&partnerID=8YFLogxK
U2 - 10.1007/s00366-024-02012-z
DO - 10.1007/s00366-024-02012-z
M3 - Article
AN - SCOPUS:85200997884
VL - 40
SP - 4023
EP - 4041
JO - Engineering with computers
JF - Engineering with computers
SN - 0177-0667
IS - 6
M1 - 114115
ER -