| 赵敏,陈文.基于径向基函数的加权最小二乘无网格法[J].计算力学学报,2011,28(1):66~71 |
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| 基于径向基函数的加权最小二乘无网格法 |
| A meshless weighted least square method based on radial basic functions |
| 投稿时间：2009-02-04 修订日期：2010-03-30 |
| DOI：10.7511/jslx201101013 |
| 中文关键词: 无网格法 径向基函数 MQ 加权最小二乘法 |
| 英文关键词:meshless method radial basic function MQ weighted least-square method |
| 基金项目:国家自然科学基金面上项目(10672051)资助项目. |
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| 中文摘要: |
| 径向基函数插值是一种新型的无网格插值方法,具有形式简单、空间维数无关等优点。这种插值方法具有δ函数的性质,易于满足本质边界条件,且插值函数的导数求解过程比通常的移动最小二乘插值(MLS)简单,精度也较高。另一方面,通过加权最小二乘法离散控制方程不需要积分,具有效率高,精度高等优点。本文试图将两者的优点结合起来,发展一种新型的无网格方法-基于径向基函数的加权最小二乘无网格法。针对弹性静力学问题的数值试验表明,这种方法具有较高的精度和稳定性。 |
| 英文摘要: |
| Radial basic function is a recent meshless interpolation technique. It has a very simply form and no correlation with the space dimensions. The RBF shape functions possess the δ function property and can easily satisfy the essential boundary condition, and their derivatives are much easier to obtain compared to that of the moving least square shape function. The RBF interpolation accuracy is also found very high. Weight Least Square Method (WLSM ) is a new meshless method. It uses the Weighted Least Square Form to discrete the government function, so it needn’t the integration, and have high accuracy, high efficiency and some other advantages. In this study, we develop a new meshless method in the combination of the advantages of these two methods. The present method is tested to elastic static problems. And results show that this method is stable and accurate. |
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