Universal Monte-Carlo algorithm for extracting electrical capacitancies

In this paper we discuss problem of mutual capacity extraction using Monte-Carlo methods. For that purpose we represent capacitance coefficients as functional for outer Dirichlet problem for Laplace equation. This paper contains multipurpose algorithms, which allow calculate capacities for system of conductors if specified next functions: normal vector in the point on the cover, which separate inner object from others, and distance from this point to the nearest conductor. Time costs for calculations by this algorithms are independent from conductors' geometry. These algorithms are competitive with well-known programs FastCap and FFTCap on tasks with complex geometry. Implementations for conductors separated by spheres and canonical parallelepipeds as well as additional samples can be found at http://teachers.uni-vologda.ac.ru/stat_mod/.