摘要
无网格法是一种求解偏微分方程的有力工具,该技术具有局部化技术的无单元特性。在各种无网格法中,场函数近似采用滑动最小二乘最为常见,其在精度和前后处理等方面有着明显的计算优势。全面介绍各种滑动最小二乘近似技术和插值特点,尤其是基于奇异权函数的滑动最小二乘插值技术,并应用到无网格法中,可以自然满足Dirichlet条件,从而可以省去Lagrange乘子;同时对一、二维算例进行计算,将其结果与精确解和经典的FEM解进行比较。
Meshless method is one kind of powerful tool for numerical solutions of partial differential equations(PDEs),and it has local technique and element-free characteristics.Among the meshless methods,moving least-square approximation is most common in constructing the shape function.The meshless method has more computation advantages in such respects as accuracy and pre-processing,post-processing,etc..The paper introduces in detail the MLS technology and the interpolation characteristics,especially the MLS interpolation of singular weighted function.The Dirichlet boundary conditions are met through the use of a set of IMLS.Thus the Lagrange multipliers are eliminated.The validity,accuracy and efficiency of the method are demonstrated by comparing the results from IMLS with closed-form ones and the ones from FEM in 1D,2D examples.
出处
《岩石力学与工程学报》
EI
CAS
CSCD
北大核心
2006年第z1期3003-3008,共6页
Chinese Journal of Rock Mechanics and Engineering
基金
国家自然科学基金资助项目(40472134)
中国博士后基金(2003033168)
吉林大学创新基金资助项目(419070200043)
关键词
数值方法
奇异权函数MLS插值
形函数
无网格法
计算对比
numerical method
interpolation MLS of singular weighted function
shape function
meshless method
calculation comparison
