A study of Smoothing Methods for the Wavelet-based Algebraic Multigrid

Abstract

The Wavelet-based Algebraic Multigrid method was proposed for the solution of linear systems issued from Finite Element applications. Like in any multilevel approach, it is very important to ensure an efficient interaction between the smoother and the coarse-grid correction in the WAMG. In contrast to the standard algebraic multigrid approach, that uses some simple relaxation scheme and enforces the interaction by choosing the coarser levels and the transfer operators appropriately, the WAMG relies more strongly on the smoothing method. In order to better understand this smoother dependency, an investigation about the requirements over smoother methods in wavelet-based algebraic multigrid is accomplished in this work. Some variants of the Gauss-Seidel and Successive Over Relaxation smoothers were tested and the magnitudes of the frequency components of the error before and after the smoother application were analyzed for an elliptic problem.