.png){kind=icon}
返回
Optimal variable shape parameter for multiquadric based RBF-FD method
.png){kind=icon}
PRE
AI
DOI：10.1016/j.jcp.2011.11.036.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
In this follow up paper to our previous study in Bayona et al. (2011)[2], we present a new technique to compute the solution of PDEs with the multiquadric based RBF finite difference method (RBF-FD) using an optimal node dependent variable value of the shape parameter. This optimal value is chosen so that, to leading order, the local approximation error of the RBF-FD formulas is zero. In our previous paper (Bayona et al., 2011) [2] we considered the case of an optimal (constant) value of the shape parameter for all the nodes. Our new results show that, if one allows the shape parameter to be different at each grid point of the domain, one may obtain very significant accuracy improvements with a simple and inexpensive numerical technique. We analyze the same examples studied in Bayona et al. (2011)[2], both with structured and unstructured grids, and compare our new results with those obtained previously. We also find that, if there are a significant number of nodes for which no optimal value of the shape parameter exists, then the improvement in accuracy deteriorates significantly. In those cases, we use generalized multiquadrics as RBFs and choose the exponent of the multiquadric at each node to assure the existence of an optimal variable shape parameter. (C) 2011 Elsevier Inc. All rights reserved.
Keyword:
Radial basis functions
Multiquadric
Mesh-free
Shape parameter
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
3.8
论文数:
1.6W
被引数:
7.4W
机构
引用论文
Residual Structure in Islet Amyloid Polypeptide Mediates Its Interactions with Soluble Insulin.png)
Biochemistry
BiochemistryIF0
PREAI
分享收藏Local radial basis function based gridfree scheme for unsteady incompressible viscous flows基于局部径向基函数的非定常不可压缩粘性流的无网格方案
PREAI
分享收藏
分享收藏
查看更多内容