A new multilevel smoothing method for wavelet-based algebraic multigrid poisson problem solver

• Main Authors: Fabio Henrique Pereira, Kleber Rogério Moreira Prado, Silvio Ikuyo Nabeta
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Microondas e Optoeletrônica; Sociedade Brasileira de Eletromagnetismo
• Series: Journal of Microwaves, Optoelectronics and Electromagnetic Applications
• Subjects: Algebraic Multigrid; Gauss-Seidel Method; Multilevel Smoother; Poisson Problem; Projection Technique; Smoothing Method
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2179-10742011000200008&lng=en&tlng=en

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.