Isogeometric analysis of minimal surfaces on the basis of extended Catmull–Clark subdivision

Qing Pan, Timon Rabczuk, Chong Chen, Guoliang Xu, Kejia Pan

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)

Abstract

We study the application of Isogeometric Analysis based on extended Catmull–Clark subdivision approach for the minimal surface models on planar domains. Subdivision approaches are compatible with NURBS as the standard of CAD systems which are capable of the refinability of B-spline techniques. The exactness of the physical domain of interest is fixed patchwise by the coarsest quadrilateral mesh and maintained through refinement. By performing extended Catmull–Clark subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of bicubic splines while maintaining its original exactness. The finite element space is spanned by the limit form of extended Catmull–Clark subdivision, which possesses C1 smoothness and the flexibility of mesh topology. In this work we establish the approximation properties and inverse inequalities for this space which are similar to the ones of classical finite elements. The approximation estimates for the minimal surface models are developed with the aid of the H1-norm convergence property of its linearization model. The performance of numerical tests is consistent with the theoretical results. We also compare these numerical calculations with classical linear finite element methods.

Original languageEnglish
Pages (from-to)128-149
Number of pages22
JournalComputer Methods in Applied Mechanics and Engineering
Volume337
DOIs
Publication statusPublished - 2018 Aug 1
Externally publishedYes

Bibliographical note

Funding Information:
We would like to thank Prof. Chuanmiao Chen from the College of Mathematics and Computer Science at Hunan Normal University, for his helpful discussions and comments. Qing Pan is supported by National Natural Science Foundation of China (NSFC) (No. 11671130), Scientific Research Fund of Hunan Provincial Education Department (No. 15A110) and Hunan Provincial Natural Science Foundation of China (No. 2018JJ2248). Chong Chen is supported by National Natural Science Foundation of China (NSFC) (No. 11301520). Kejia Pan is supported by National Natural Science Foundation of China (NSFC) (No. 41474103), the Excellent Youth Foundation of Hunan Province of China (No. 2018JJ1042) and the Innovation-Driven Project of Central South Univeristy (No. 2018CX042).

Funding Information:
We would like to thank Prof. Chuanmiao Chen from the College of Mathematics and Computer Science at Hunan Normal University, for his helpful discussions and comments. Qing Pan is supported by National Natural Science Foundation of China (NSFC) (No. 11671130 ), Scientific Research Fund of Hunan Provincial Education Department (No. 15A110 ) and Hunan Provincial Natural Science Foundation of China (No. 2018JJ2248 ). Chong Chen is supported by National Natural Science Foundation of China (NSFC) (No. 11301520 ). Kejia Pan is supported by National Natural Science Foundation of China (NSFC) (No. 41474103 ), the Excellent Youth Foundation of Hunan Province of China (No. 2018JJ1042 ) and the Innovation-Driven Project of Central South Univeristy (No. 2018CX042 ).

Keywords

  • Error estimation
  • Extended Catmull–Clark subdivision
  • Isogeometric analysis
  • Minimal surfaces

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy
  • Computer Science Applications

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