  It is shown how various ideas that are well established for the solution of
Poisson's equation using plane wave and multigrid methods can be combined with
wavelet concepts. The combination of wavelet concepts and multigrid techniques
turns out to be particularly fruitful. We propose a modified multigrid V cycle
scheme that is not only much simpler, but also more efficient than the standard
V cycle. Whereas in the traditional V cycle the residue is passed to the
coarser grid levels, this new scheme does not require the calculation of a
residue. Instead it works with copies of the charge density on the different
grid levels that were obtained from the underlying charge density on the finest
grid by wavelet transformations. This scheme is not limited to the pure wavelet
setting, where it is faster than the preconditioned conjugate gradient method,
but equally well applicable for finite difference discretizations.
