A novel pseudospectral Fourier method for solving Poissonʹs equation for a solute in a non-uniform dielectric Original Research Article

A novel pseudospectral method is presented for solving Poissonʹs equation for a solute in a non-uniform dielectric. Poissonʹs equation is transformed to a Helmholtz-like equation which is solved iteratively, as a linear system of equations, by introducing a grid and employing fast Fourier transforms. Several algorithms have been tested for solution of the linear system, and application of an appropriately preconditioned linear solver has been found to provide a robust, rapidly convergent procedure. The method scales nearly linearly with system size, and its implementation is straightforward. Application of the method is demonstrated for computation of the electrostatic contribution to the solvation energy for a wide range of solute molecules, and convergence of the method is shown to be nearly independent of solute and grid size.