Multilevel wavelet solver for the Ornstein-Zernike equation

A multilevel wavelet algorithm is developed to solve integral equations for the pair correlations in simple liquids. The algorithm is based on the discrete wavelet transform of the radial correlation functions. The fundamental properties of wavelet bases are employed to improve the convergence and speed of the algorithm. The Coifman 2 basis set is used for the wavelet treatment. To solve the Ornstein-Zernike integral equations we have applied a combined scheme in which the coarse part of the solution is calculated with the use of wavelets by a multilevel method, and the fine part by Picard iteration. We report on numerical experiments which show that the proposed procedure is more effective than one in which the coarse grid solution is computed by a single-level iteration.