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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 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.
Key
words: Wavelet
finite element(WFE) Multiresolution Adaptive Singularity
CLC No: TB21
TH12
国家自然科学基金(50335030)、高校博士点专项基金(20040698026)资助项目.
Received 20040816, received in revised form 20050120
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