Journal of Applied Mathematics
Volume 2012 (2012), Article ID 894074, 15 pages
Research Article

A Parallel Wavelet-Based Algebraic Multigrid Black-Box Solver and Preconditioner

1Industrial Engineering Post Graduation Program, Nove de Julho University (PMEP/UNINOVE), Francisco Matarazzo Avenue, 612, 05001100 São Paulo, SP, Brazil
2Electrical Machine and Drives Lab, São Paulo University (GMAcq/EP/USP), Luciano Gualberto Avenue, 380, 05508-010 São Paulo, SP, Brazil

Received 1 November 2011; Revised 26 January 2012; Accepted 8 February 2012

Academic Editor: Massimiliano Ferronato

Copyright © 2012 Fabio Henrique Pereira and Sílvio Ikuyo Nabeta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work introduces a new parallel wavelet-based algorithm for algebraic multigrid method (PWAMG) using a variation of the standard parallel implementation of discrete wavelet transforms. This new approach eliminates the grid coarsening process in traditional algebraic multigrid setup phase simplifying its implementation on distributed memory machines. The PWAMG method is used as a parallel black-box solver and as a preconditioner in some linear equations systems resulting from circuit simulations and 3D finite elements electromagnetic problems. The numerical results evaluate the efficiency of the new approach as a standalone solver and as preconditioner for the biconjugate gradient stabilized iterative method.