A fast solver for the Ornstein–Zernike equations

In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein–Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson–Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.