Random walk approach to wave radiation in cylindrical and spherical domains

Two- and three-dimensional Helmholtz equations in the exterior cylindrical and spherical domains are addressed by the random walk method. The solutions of the Dirichlet problems in such domains are represented as mathematical expectations of specified functionals on trajectories of random motions running in designated domains of a multi-dimensional complex space. The numerical examples confirm the efficiency of the random walk approach to the analysis of wave radiation.