In contrast to the standard algebraic multigrid, the
Wavelet-based Algebraic Multigrid method relies more strongly on
the smoothing method because the coarse spaces are chosen a
priori. So, it is very important to develop new smoother methods,
especially for those cases where the classical Gauss-Seidel
smoothing method does not give good results. This paper proposes a
new multilevel smoothing approach based on projection technique.
The proposed smoothing method was applied to smoothing the
error in a linear systems issued from finite element solutions of the
elliptic equation and the results compared with those obtained from
the Gauss-Seidel method.
