Abstract
A wavelet-based preconditioning technique for conjugate gradient Poisson solvers is described. While the linear systems can be solved with an iterative matrix solver, the convergence speed becomes worse and the computing time increases with increase of grid points. The problem, however, can be solved by our preconditioning method using wavelets. In this paper, we specially pay attention to the application of Haar wavelets. Since the discrete wavelet transform has a good property in data locality, our algorithm can take advantage of parallel processing capabilities and enhance parallel performance, unlike many other preconditioning methods which are not suitable for vector and parallel processing. These kinds of combined approaches of software and hardware are superior in large-scale problems and will play more important roles in future computational science.
