An iterative algorithm based on fast-Fourier transforms is presented that solves the equations of continuum electrostatics for systems of heterogeneous dielectric permittivity (e.g., solute cavity in a solvent) under periodic boundary conditions. The method makes explicit use of the charge-dipole and dipole-dipole interaction tensors, and is thus applicable both to Coulombic interactions (Ewald scheme) and cutoff-based electrostatic interactions described by any polynomial function (including a Coulombic r(-1) term), as commonly used in molecular dynamics simulations. The latter case includes, in particular, straight truncation of Coulombic interactions and truncation including a reaction-field correction. After testing and validation by comparison with existing methods, the algorithm is used to investigate the effect of cutoff truncation and artificial periodicity in explicit-solvent simulations of ionic solvation and ion-ion interactions. Both cutoff truncation and artificial periodicity are found to significantly affect the polarization around a spherical ion and its solvation free energy. The nature and magnitude of the two perturbations are analyzed in detail, and approximate analytical correction terms are derived to be applied to the results of explicit-solvent simulations. Cutoff truncation induces strong alterations in the potential of mean force for the interaction between two spherical ions. The present observations based on continuum electrostatics help to rationalize artifacts previously reported from explicit-solvent simulations involving cutoff truncation and, in particular, the unphysical attraction of like charges and repulsion of opposite charges, and the corresponding alterations in the relative stabilities of contact, solvent-separated, and free ion pairs. (C) 2003 American Institute of Physics.