| 新型滑动最小二乘技术的实现及其在无网格法中应用 | |
| 张延军 ; 王恩志 ; ZHANG Yanjun ; WANG Enzhi | |
| 2010-06-10 ; 2010-06-10 | |
| 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 TU45 |
| 其他题名 | NEW IMPLEMENT OF MOVING LEAST-SQUARE TECHNOLOGY AND ITS APPLICATION IN MESHLESS METHOD |
| 中文摘要 | 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.; 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) |
| 语种 | 中文 ; 中文 |
| 内容类型 | 期刊论文 |
| 源URL | [http://hdl.handle.net/123456789/59939]  |
| 专题 | 清华大学 |
| 推荐引用方式 GB/T 7714 | 张延军,王恩志,ZHANG Yanjun,等. 新型滑动最小二乘技术的实现及其在无网格法中应用[J],2010, 2010. |
| APA | 张延军,王恩志,ZHANG Yanjun,&WANG Enzhi.(2010).新型滑动最小二乘技术的实现及其在无网格法中应用.. |
| MLA | 张延军,et al."新型滑动最小二乘技术的实现及其在无网格法中应用".(2010). |
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