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MiS Preprint
88/2008

A multigrid solver for the integral equations of the theory of liquids

Maxim V. Fedorov and Wolfgang Hackbusch

Abstract

In this article we present a new multigrid algorithm to solve the Ornstein-Zernike type integral equations of the theory of liquids. This approach is based on ideas coming from the multigrid methods for numerical solutions of integral equations (see paragraph 16 in [13]). We describe this method in a general manner as a 'template' for construction of efficient multilevel iterations for numerical solution of the integral equations in the theory of liquids. We report on several numerical experiments to illustrate the effectiveness of the method. The algorithm is tested on a model problem - a simple monoatomic fluid with a continuous short ranged potential. The tests have indicated that the method sufficiently accelerates the convergence of the numerical solution in all considered cases.

Received:
Dec 14, 2008
Published:
Dec 16, 2008
MSC Codes:
65R99, 45G15
Keywords:
multigrid methods, ornstein-zernike equation, integral equations theory of liquids

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Preprint
2008 Repository Open Access
Maxim V. Fedorov and Wolfgang Hackbusch

A multigrid solver for the integral equations of the theory of liquids