Calculation of mutual capacitances for system of conductors in dielectric media using “walk on hemispheres”

In this paper we discuss the problem of mutual capacitance extraction for system of conductors in inhomogeneous isotropic dielectrics using Monte-Carlo method. For that purpose we represent capacitance coefficients as functional for outer Dirichlet problem for Laplace equation. Unbiased and low-biased estimates are constructed using “walk on hemispheres” process. Algorithm can be used for calculating mutual capacities for systems of conductors in inhomogeneous isotropic dielectrics with plain dielectric interfaces. To use it one need to define functions for: generating uniformly distributed point on the “shell”, that separate inner object from others; finding of normal vector in the point on the “shell”, on the conductor and at dielectric interface; calculation of distance from specified point to nearest conductor and nearest dielectric interface; finding dielectric permittivity at the given point. The paper contains results of experiments for parallelepiped conductors separated with parallelepiped “shells”.