Efficient algorithms for electrostatic interactions including dielectric contrasts (Q280666)

The authors consider the problem of computing numerically the electrostatic potential or the electrostatic field for charge distributions in media with different dielectric properties. Thus discontinuities of the relative permittivity occur at interfaces. The Poisson equation with appropriate boundary conditions identifies the electrostatic potential. Applications and test examples stem from molecular dynamics and nanoscale systems, for example.NEWLINENEWLINEThis paper reviews numerical methods and results, which were mostly published before by the authors. Firstly, a multi-body method called MMM2D was investigated in [\textit{A. Arnold} and \textit{C. Holm}, ``MMM2D: A fast and accurate summation method for electrostatic interactions in 2D slab geometries'', Comput. Phys. Commun. 148, No. 3, 327--348 (2002; \url{doi:10.1016/S0010-4655(02)00586-6})]. This approach applies specific periodic boundary conditions in the case of planar interfaces. The technique is modified by the introduction of image charges. Secondly, an induced charge calculation (ICC) technique is considered for interfaces with arbitrary shape, see [\textit{S. Kesselheim} et al., Comput. Phys. Commun. 182, No. 1, 33--35 (2011; Zbl 1216.92008)]. This strategy represents a boundary element method using Green's function for the Laplace operator. Modifications of both approaches are discussed to simulate metallic interfaces. Thirdly, a method called Maxwell equations molecular dynamics (MEMD) is applied to solve problems in the case of smoothly varying permittivity. All presented algorithms are available in open source simulation packages.NEWLINENEWLINEConcerning each method, the authors present a computer simulation of an example from physical or technical applications. Therein, the different properties of the physical behaviour are observed. The comparison of the efficiency for several numerical methods applied to the same example are not within the scope of the paper, except for some discussion given in the case of metallic boundaries.