THE FAST MULTIPOLE BOUNDARY-ELEMENT METHOD FOR MOLECULAR ELECTROSTATICS - AN OPTIMAL APPROACH FOR LARGE SYSTEMS

We propose a fast implementation of the boundary element method for so lving the Poisson equation, which approximately determines the electro static 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 mol ecular surface. The method is based on the Fast Multipole Algorithm by Rokhlin and Greengard, which is used to calculate the Coulombic inter action between surface elements in linear time. We calculate the solva tion energies of a sphere, a small polar molecule, and a moderately si zed protein. The values obtained by the boundary element method agree well with results from finite difference calculations and show a highe r degree of consistency due to the absence of grid dependencies. The b oundary element method can be taken to a much higher accuracy than is possible with finite difference methods and can therefore be used to v erify their validity. (C) 1995 by John Wiley and Sons, Inc.