W. Sweldens, “The Lifting Scheme: A Construction of Second Generation Wavelets,” SIAM Journal on Mathematical Analysis, Vol. 29, No. 2, 1997, pp. 511-546. doi:10.1137/S0036141095289051
has been cited by the following article:
TITLE: A Wavelet Multigrid Method Using Symmetric Biorthogonal Wavelets
AUTHORS: Doreen De Leon
KEYWORDS: Multigrid; Wavelets; Biorthogonal Wavelets
JOURNAL NAME: American Journal of Computational Mathematics, Vol.3 No.2, June 24, 2013
ABSTRACT: In [1], the author introduced a wavelet multigrid method that used the wavelet transform to define the coarse grid, interpolation, and restriction operators for the multigrid method. In this paper, we modify the method by using symmetric biorthogonal wavelet transforms to define the requisite operators. Numerical examples are presented to demonstrate the effectiveness of the modified wavelet multigrid method for diffusion problems with highly oscillatory coefficients, as well as for advection-diffusion equations in which the advection is moderately dominant.