| 基于径向基函数的点插值(RPIM)无网格法 |
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| 引用本文： | 夏茂辉,贾延,刘才.基于径向基函数的点插值(RPIM)无网格法[J].燕山大学学报,2006,30(2):112-117. |
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| 作者姓名： | 夏茂辉 贾延 刘才 |
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| 作者单位： | 1. 燕山大学,理学院,河北,秦皇岛,066004
2. 燕山大学,机械工程学院,河北,秦皇岛,066004 |
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| 摘 要： | 基于径向函数的点插值法（RPIM）是一种新型无网格法。它有效地解决了点插值法（PIM）中遇到的最大困难：系数矩阵奇异性问题。此外，由于插值具有巧函数的性质，从而克服了以往无网格法中难以实现的位移边界条件的难点。本文简单介绍了PIM，重点阐述了RPIM的基本原理，并用算例表明了该法具有效率高、精度高和稳定性好等优点，在工程中具有广阔的应用前景。
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| 关 键 词： | 无网格法 点插值法 径向基函数 |
| 文章编号： | 1007-791X(2006)02-0112-06 |
| 修稿时间： | 2005年4月20日 |
A meshless method with radial point interpolation method (RPIM) |
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| XIA Mao-hui,JIA Yan,LIU Cai.A meshless method with radial point interpolation method (RPIM)[J].Journal of Yanshan University,2006,30(2):112-117. |
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| Authors: | XIA Mao-hui JIA Yan LIU Cai |
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| Abstract: | A Point interpolation method which base on the basis function is a new meshless method. It is advantageous over the meshless methods based on moving least square (MLS) methods in implementation of esstionial boundary condition and over the original PIM with polynomial basis in avoiding singularity when shape functions are constructed. In this paper, the basic principle of PIM and RPIM is introduced. In addition, numerical example shows that the new methods possess several advantages, such as high accuracy, high stability and high efficiency. It is a promising method in engineering. |
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| Keywords: | meshless methods point interpolation method radial basis functions |
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