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An Efficient Adaptive Wavelet-Collocation Method Using Lifted Interpolating Wavelets

수정된 보간 웨이블렛응 이용한 적응 웨이블렛-콜로케이션 기법

  • Published : 2000.08.01

Abstract

The wavelet theory is relatively a new development and now acquires popularity and much interest in many areas including mathematics and engineering. This work presents an adaptive wavelet method for a numerical solution of partial differential equations in a collocation sense. Due to the multi-resolution nature of wavelets, an adaptive strategy can be easily realized it is easy to add or delete the wavelet coefficients as resolution levels progress. Typical wavelet-collocation methods use interpolating wavelets having no vanishing moment, but we propose a new wavelet-collocation method on modified interpolating wavelets having 2 vanishing moments. The use of the modified interpolating wavelets obtained by the lifting scheme requires a smaller number of wavelet coefficients as well as a smaller condition number of system matrices. The latter property makes a preconditioned conjugate gradient solver more useful for efficient analysis.

Keywords

Wavelet;Multi-Resolution Analysis;interpolating Wavelet;Lifting Scheme;Boundary Wavelet;Preconditioned Conjugate Gradient Method;Adaptive Algorithm;Thresholding Parameter

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