摘要
利用张量积构造正则空间,用于场函数逼近,得到MLS(moving least squares)场函数插值形式的一个特例.在规则域上,通过基空间扩张,构造满足齐次边界条件的场函数,使得MLS插值形式变得更简单有效,扩大了基函数空间的选择范围,克服了一般MLS逼近所特有的大量求逆、计算效率低下、判据复杂的缺点.数值实例表明,该方法数学概念简单,加密点阵重复计算方便,计算精度高,计算结果连续性好,总体计算量少,计算过程收敛快.
Normalized space constructed by tensor product was used in field function approach to give a special case of moving least squares （MLS） interpolation scheme. In the regular domain, The field function which meets homogenous boundary conditions was constructed by spanning base space to make the MLS interpolation scheme simpler and more efficient. Owing to expanded basis functions＇ selection, some drawbacks in general MLS method, for example repeated inversion, low calculation efficiency, and complex criterions, can be avoided completely. Numerical examples illustrate that the proposed method is characterized by simple mathematical concept, convenient repeat calculations with high accuracy, good continuity, less computation and rapid convergence.
出处
《华中科技大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2007年第2期8-11,共4页
Journal of Huazhong University of Science and Technology(Natural Science Edition)
基金
中国科学院岩土力学重点实验室开放基金资助项目(Z110507)
关键词
权函数
张量积
正则空间
广义变分原理
weighted function
tensor product
normalized space
general variational principle
