A new Monte Carlo method for Neumann problems

The Monte Carlo methods (MCMs) have been applied with great success to the solution of the elliptic differential equation, but none of them in their present form can be used when a mixed boundary condition is involved. To overcome this limitation existing in classical MCMs, a new fixed random walk method, known as the triangular mesh random walk method, is presented for the elliptical problem with mixed boundary condition. This method can be used to solve many electromagnetic field problems. The numerical calculation involving some two-dimensional problems confirms the efficiency of triangular mesh random walk method.