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An Efficient Adaptive Wavelet-Collocation Method Using Lifted Interpolating Wavelets
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 Title & Authors
An Efficient Adaptive Wavelet-Collocation Method Using Lifted Interpolating Wavelets
Kim, Yun-Yeong; Kim, Jae-Eun;
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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.
Wavelet;Multi-Resolution Analysis;interpolating Wavelet;Lifting Scheme;Boundary Wavelet;Preconditioned Conjugate Gradient Method;Adaptive Algorithm;Thresholding Parameter;
 Cited by
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