Electrostatic field calculation of multi-particle systems with and without contact points by the surface charge simulation method

This paper describes three-dimensional electrostatic field calculations in multi-particle systems by a surface charge simulation method (SCM), one of the integral equation methods, sometimes called the indirect boundary element method. The utilized SCM adopts the fast multipole method (FMM), an O(N) algorithm for solving a dense linear system appearing in the SCM, where N is the number of unknowns. The calculated arrangements consist of spherical dielectrics, the radius of which is 1cm, in the form of (a) a string of beads (2 to 12 particles) or (b) a simple three-dimensional lattice (2³ or 10³ particles) under a homogeneous applied field. The half-length of the gap between the particles is (i) zero (with contact points) or (ii) 0.01cm to 0.5cm (without contact points). The charge and field distributions on the particles are numerically determined using up to 432000 curved triangular elements and 866000 unknowns in the quadratic basis function.