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An integral equation approach to calculate electrostatic interactions in many-body dielectric systems. (English) Zbl 1415.78002

Summary: In this article, a numerical method to compute the electrostatic interaction energy and forces between many dielectric particles is presented. The computational method is based on a Galerkin approximation of an integral equation formulation, which is sufficiently general, as it is able to treat systems embedded in a homogeneous dielectric medium containing an arbitrary number of spherical particles of arbitrary size, charge, dielectric constant and position in the three-dimensional space. The algorithmic complexity is linear scaling with respect to the number of particles for the computation of the energy which has been achieved through the use of a modified fast multipole method. The method scales with the third power of the degree of spherical harmonics used in the underlying expansions, for general three-dimensional particle configurations. Several simple numerical examples illustrate the capabilities of the model, and the influence of mutual polarization between particles in an electrostatic interaction is discussed.

MSC:

78A35 Motion of charged particles
78A30 Electro- and magnetostatics
78M16 Multipole methods applied to problems in optics and electromagnetic theory
65R20 Numerical methods for integral equations
65Z05 Applications to the sciences

Software:

ScalFMM
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Full Text: DOI

References:

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