title: An efficient algorithm for classical density functional theory in three dimensions: ionic solutions.
abstract: Classical density functional theory (DFT) of fluids is a valuable tool to analyze inhomogeneous fluids. However, few numerical solution algorithms for three-dimensional systems exist. Here we present an efficient numerical scheme for fluids of charged, hard spheres that uses O(N log N) operations and O(N) memory, where N is the number of grid points. This system-size scaling is significant because of the very large N required for three-dimensional systems. The algorithm uses fast Fourier transforms (FFTs) to evaluate the convolutions of the DFT Euler-Lagrange equations and Picard (iterative substitution) iteration with line search to solve the equations. The pros and cons of this FFT/Picard technique are compared to those of alternative solution methods that use real-space integration of the convolutions instead of FFTs and Newton iteration instead of Picard. For the hard-sphere DFT, we use fundamental measure theory. For the electrostatic DFT, we present two algorithms. One is for the "bulk-fluid" functional of Rosenfeld [Y. Rosenfeld, J. Chem. Phys. 98, 8126 (1993)] that uses O(N log N) operations. The other is for the "reference fluid density" (RFD) functional [D. Gillespie et al., J. Phys.: Condens. Matter 14, 12129 (2002)]. This functional is significantly more accurate than the bulk-fluid functional, but the RFD algorithm requires O(N(2)) operations.
authors.affiliation: Computation Institute, University of Chicago, Chicago, Illinois 60637, USA. knepley@ci.uchicago.edu
authors.forename: Matthew G
authors.initials: MG
authors.lastname: Knepley
authors.forename: Dmitry A
authors.initials: DA
authors.lastname: Karpeev
authors.forename: Seth
authors.initials: S
authors.lastname: Davidovits
authors.forename: Robert S
authors.initials: RS
authors.lastname: Eisenberg
authors.forename: Dirk
authors.initials: D
authors.lastname: Gillespie
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D007477:Ions / Q000737:chemistry*; D011789:Quantum Theory; D012996:Solutions / Q000737:chemistry; D055672:Static Electricity
chemical_list: D007477:Ions; D012996:Solutions