Higher-order discretised boundary conditions at edges for TE waves

One of the important aspects in the solution of field problems using numerical techniques such as the finite difference method is the accurate description of the field singularity behaviour near a sharp edge. The authors propose higher-order discretised boundary conditions at the edges of perfectly conducting wedges for transverse electric waves. The boundary conditions are derived through discretisation of the field expressions that already satisfy the Helmholtz equation and the edge condition in the vicinity of the edges and thus can properly characterise the field behaviours there. Numerical results show high accuracy and stability of the treatment.