Freespace boundary conditions for Poisson´s equation in 2D

In computationally modeling domains using Poisson´s equation for electrostatics or magnetostatics, it is often desirable to have open boundaries that extend to infinity. In electrostatics, the normal component of the electric field is often set to zero using system boundaries sufficiently far as to make this approximation accurate. In magnetostatics, imposing that the normal component goes to zero is equivalent to the ideal conductor boundary condition. It is noted that the configuration and strength of field lines is dependent upon the size of the boundary chosen, and an infinitely large grid is required to resolve the problem. To resolve this difficulty, a method based upon using a finite amount of terms of the solution to Laplace´s equation outside the boundary is introduced. The solution to the Laplace equation outside the domain is coupled with the system of finite difference equations and a finite difference expression for the normal derivative at the boundary.