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The fast multipole boundary element method for molecular electrostatics: An optimal approach for large systems
Author(s) -
Bharadwaj Ranganathan,
Windemuth Andreas,
Sridharan S.,
Honig Barry,
Nicholls Anthony
Publication year - 1995
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540160707
Subject(s) - boundary element method , multipole expansion , boundary knot method , fast multipole method , solvation , boundary (topology) , electrostatics , poisson's equation , finite element method , boundary value problem , physics , computational physics , mathematical analysis , mathematics , molecule , quantum mechanics , thermodynamics
We propose a fast implementation of the boundary element method for solving the Poisson equation, which approximately determines the electrostatic field around solvated molecules of arbitrary shape. The method presented uses computational resources of order O ( N ) only, where N is the number of elements representing the dielectric boundary at the molecular surface. The method is based on the Fast Multipole Algorithm by Rokhlin and Greengard, which is used to calculate the Coulombic interaction between surface elements in linear time. We calculate the solvation energies of a sphere, a small polar molecule, and a moderately sized protein. The values obtained by the boundary element method agree well with results from finite difference calculations and show a higher degree of consistency due to the absence of grid dependencies. The boundary element method can be taken to a much higher accuracy than is possible with finite difference methods and can therefore be used to verify their validity. © 1995 by John Wiley & Sons, Inc.