Solving Laplace equation with Dirichlet boundary value condition by R-functions method taking into account symmetry

In this paper a case of punctual symmetry of cyclic type and application R-functions method to building equations of the boundary of symmetry objects are considered. R-functions method combine with Ritz method for solving Laplace equation in complicated domain that has symmetry is using. The problem of calculation an electrostatic field in system with the crossed fields (reversed construction cylindrical magnetron) is considered.