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Real-Space Mesh Techniques in Molecular Theory of 3D Solvation
To provide fast computation of the 3D solvation in molecular liquids, we develop a new computational approach based on real-space mesh techniques. Basic aspects and peculiarities of this approach are presented within the framework of the integral equation theory of molecular liquids. Starting from the free energy functional of the 3D solvation problem, we reformulate the integral equations in terms of the solvent induced potential. As a result, we reduce the problem to evaluation of the volume integrals in the interface region. We perform a domain decomposition of the region in terms of finite elements consisting from of the relevant surface elements built from scaled solvent accessible surfaces. The Chebyshev polynomials are found to be the most suitable for accurate approximation of the sought-for functions for these finite elements. The tensor product approximation and the nonequispaced fast fourier transform are proposed to be applied for fast evaluation of the relevant kernel of the integral equations. The computational complexity of the calculations are supposed to be reduced by thousand times with respect to current algorithms of the molecular solvation, which are based on the uniform fast fourier transform.