摘要
小波有限元是一类新的有限元逼近方法,将信号处理领域中小波函数的多分辨思想引入有限元法中,以小波函数作为插值函数,构造出嵌套递进的多尺度广义有限元逼近空间,使得求解问题可以先用较粗的网格分析,特定奇异区域通过自适应多分辨剖分获得更好的逼近,该算法数值稳定性好、适宜求解奇异性问题。从小波加权残值法、小波有限元理论以及自适应小波有限元三个方面,综述了小波有限元国内外研究现状,并介绍了小波有限元在大梯度非线性、裂纹定量预示等方面的工程应用进展,指出了其关键技术、存在问题以及工程实用前景。
Wavelet finite element (WFE) method is a new class of finite element approximation method. Wavelet multiresolu tion analysis theory of signal processing is introduced into finite element analysis, and nesting multiscale finite element approximation spaces are constructed by using wavelet bases as interpolating functions. Thus WFE method can yield an initial coarse description of the solution in lower order approximation space, successively refine the solution in singular regions with adaptive multiresolution. This method has good numerical stability and efficiency to singularity problems. Considering three aspects, wavelet weighted residual method, WFE theory and adaptive WFE, the recent developments of WFE method are reviewed. New progresses of engineering application, such as nonlinear large gradient, quantitative crack prognosis, are introduced. Some key techniques, unsolved problems and practical prospect in engineering are indicated.
出处
《机械工程学报》
EI
CAS
CSCD
北大核心
2005年第3期1-11,共11页
Journal of Mechanical Engineering
基金
国家自然科学基金(50335030)高校博士点专项基金(20040698026)资助项目
关键词
小波有限元
多分辨
自适应
奇异性
Wavelet finite element(WFE) Multiresolution Adaptive Singularity
