工程设计学报Issue(3)：208-211,225,5.DOI:10.3785/j.issn.1006-754X.2013.03.007
基于 Hermite 插值的解耦小波基的构造及应用
Construction and application of the decoupling wavelet bases based on Hermite interpolation
摘要
Abstract
Using the multi-resolution analysis characteristics of wavelet ,a function may be ex-pressed by a sequence of spaces which are nested and constantly expanded ,and a multi-resolution finite element space may be established .However ,there are always couplings across scales in the multi-resolution finite element space .How to eliminate the couplings is still a problem which nee-ded to be studied further .For the Euler beam ,the decoupling wavelet bases and the correspond-ing wavelet element based on Hermite interpolation were developed to solve Euler beam problem by using the orthogonality between the vanishing moment of wavelet and polynomial .The decou-pling wavelet bases may eliminate the couplings between the low resolution space and detail spaces and that among the detail spaces in different scales .Then an adaptive algorithm based on scale-decoupling was constructed . The numerical example verifies the effectiveness of the pro-posed method .关键词
Hermite插值/解耦/小波/多分辨分析Key words
Hermite interpolation/decoupling/wavelet/multi-resolution analysis分类
数理科学引用本文复制引用
魏忠斌,何育民,段志善,高攀,申鹏..基于 Hermite 插值的解耦小波基的构造及应用[J].工程设计学报,2013,(3):208-211,225,5.基金项目
国家自然科学基金资助项目（51075314）；陕西省教育厅专项科研计划项目（2010JK621）． （）
