Boundary conditions at edges

One of the important aspects in the solution of field problems using numerical techniques such as the finite difference (FD) method is the treatment of the field behavior near a sharp edge. In this paper, we propose discretized forms of the boundary conditions at the edges of wedges on the surfaces of which the homogeneous Neumann condition is imposed. The boundary conditions are derived through discretization of the field expressions that already satisfy the edge condition in the vicinity of the edges and thus can properly characterize the field behaviors there. Numerical results show the validity and high accuracy of the present treatment.