Monte-Carlo method for discrete inhomogeneous problems

An extension of the Monte-Carlo method, applied to the numerical solution of electrostatic problems with Dirichlet conditions and various dielectric media, is proposed. Using a conventional Monte-Carlo method for each medium and the boundary conditions, a linear system of algebraic equations for the potentials at the interfaces separating two media is obtained. Once the linear system is solved, the problem is reduced to so many homogeneous Dirichlet problems in different media. A substantial reduction in computation time for the calculation of the potentials at the interface is observed compared with another Monte-Carlo approach; also, the same order of precision is obtained.