工程设计学报
工程設計學報
공정설계학보
JOURNAL OF ENGINEERING DESIGN
2013年
3期
208-211,225
,共5页
魏忠斌%何育民%段志善%高攀%申鹏
魏忠斌%何育民%段誌善%高攀%申鵬
위충빈%하육민%단지선%고반%신붕
Hermite插值%解耦%小波%多分辨分析
Hermite插值%解耦%小波%多分辨分析
Hermite삽치%해우%소파%다분변분석
Hermite interpolation%decoupling%wavelet%multi-resolution analysis
小波的多分辨分析特性使得我们可以采用逐级嵌套,不断扩大的一系列空间来逼近一个函数,建立一个多分辨的有限元空间。但是,在多分辨的有限元空间中的不同尺度空间之间常常存在耦合项,如何消除这些耦合项以构造更为有效的自适应算法仍然是一个需要深入研究的问题。对于欧拉梁问题,利用小波的消失矩与多项式的正交关系,构造了基于Hermite插值的解耦小波基及相应的小波单元,消除了低分辨逼近空间与细节空间以及各个细节空间之间耦合项,实现了基于空间尺度解耦的自适应算法。数值算例验证了该方法的有效性。
小波的多分辨分析特性使得我們可以採用逐級嵌套,不斷擴大的一繫列空間來逼近一箇函數,建立一箇多分辨的有限元空間。但是,在多分辨的有限元空間中的不同呎度空間之間常常存在耦閤項,如何消除這些耦閤項以構造更為有效的自適應算法仍然是一箇需要深入研究的問題。對于歐拉樑問題,利用小波的消失矩與多項式的正交關繫,構造瞭基于Hermite插值的解耦小波基及相應的小波單元,消除瞭低分辨逼近空間與細節空間以及各箇細節空間之間耦閤項,實現瞭基于空間呎度解耦的自適應算法。數值算例驗證瞭該方法的有效性。
소파적다분변분석특성사득아문가이채용축급감투,불단확대적일계렬공간래핍근일개함수,건립일개다분변적유한원공간。단시,재다분변적유한원공간중적불동척도공간지간상상존재우합항,여하소제저사우합항이구조경위유효적자괄응산법잉연시일개수요심입연구적문제。대우구랍량문제,이용소파적소실구여다항식적정교관계,구조료기우Hermite삽치적해우소파기급상응적소파단원,소제료저분변핍근공간여세절공간이급각개세절공간지간우합항,실현료기우공간척도해우적자괄응산법。수치산례험증료해방법적유효성。
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 .