A Wavelet Multigrid Method Using Symmetric Biorthogonal Wavelets

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.