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

Maxim V. Fedorov and Wolfgang Hackbusch

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Submission date: 14. Dec. 2008
Pages: 13
Bibtex
MSC-Numbers: 65R99, 45G15
Keywords and phrases: multigrid methods, ornstein-zernike equation, integral equations theory of liquids
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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.