• CN：11-2187/TH
• ISSN：0577-6686

›› 2005, Vol. 41 ›› Issue (3): 1-11.

• 论文 •

小波有限元理论研究与工程应用的进展

1. 西安交通大学机械制造系统工程国家重点实验室
• 发布日期:2005-03-15

ADVANCES IN THEORY STUDY AND ENGINEERING APPLICATION OF WAVELET FINITE ELEMENT

He Zhengjia;Chen Xuefeng

1. State Key Lab for Manufacturing Systems Engineering, Xi’an Jiaotong University
• Published:2005-03-15

Abstract: Wavelet finite element (WFE) method is a new class of finite element approximation method. Wavelet multiresolution analysis theory of signal processing is introduced into finite element analysis, and nesting multiscale finite element ap-proximation 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 sta-bility 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 in-troduced. Some key techniques, unsolved problems and practi-cal prospect in engineering are indicated.