Details
| Original language | English |
|---|---|
| Pages (from-to) | 343-357 |
| Number of pages | 15 |
| Journal | Computational Mechanics |
| Volume | 53 |
| Issue number | 2 |
| Publication status | Published - 5 Sept 2013 |
| Externally published | Yes |
Abstract
The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.
Keywords
- Compatibility, Delta property, Meshless, Partition of unity, Shepard shape function
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Ocean Engineering
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computational Theory and Mathematics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Computational Mechanics, Vol. 53, No. 2, 05.09.2013, p. 343-357.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An improved meshless Shepard and least squares method possessing the delta property and requiring no singular weight function
AU - Zhuang, Xiaoying
AU - Zhu, Hehua
AU - Augarde, Charles
N1 - Funding information: The authors gratefully acknowledge the support of Natural Science Foundation of China (NSFC 41130751), National Basic Research Program of China (973 Program: 2011CB013800), Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT, IRT1029), Shanghai Pujiang Talent Program (12PJ1409100) and Shanghai Chenguang Talent Program (12CG20).
PY - 2013/9/5
Y1 - 2013/9/5
N2 - The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.
AB - The meshless Shepard and least squares (MSLS) method and the meshless Shepard method are partition of unity based meshless interpolations which eliminate the problems by other meshless methods such as the difficulty in direct imposition of the essential boundary conditions. However, singular weight functions have to be used in both methods to enforce the approximation interpolatory, which leads to the loss of smoothness in approximation and locally oscillatory results. In this paper, an improved MSLS interpolation is developed by using dually defined nodal supports such that no singular weight function is required. The proposed interpolation satisfies the delta property at boundary nodes and the compatibility condition throughout the domain, and is capable of exactly reproducing the basis function. The computational cost of the present interpolation is much lower than the moving least-squares approximation which is probably the most widely used meshless interpolation at present.
KW - Compatibility
KW - Delta property
KW - Meshless
KW - Partition of unity
KW - Shepard shape function
UR - http://www.scopus.com/inward/record.url?scp=84893957679&partnerID=8YFLogxK
U2 - 10.1007/s00466-013-0912-1
DO - 10.1007/s00466-013-0912-1
M3 - Article
AN - SCOPUS:84893957679
VL - 53
SP - 343
EP - 357
JO - Computational Mechanics
JF - Computational Mechanics
SN - 0178-7675
IS - 2
ER -