Numerical reflecting boundary conditions and treatment of edge singularities for electromagnetic diffraction in the time domain

Boundary conditions of a rectangular cylinder are investigated in the finite-difference time domain for 2-D transverse magnetic (TM) waves. The scheme used is the scheme first proposed by R.H. Ni (1982) as a finite-volume scheme but which can also be viewed as a finite-difference scheme a la Lax-Wendroff. This scheme is solved on a computational, cell-by-cell basis and contains both the electric and magnetic field components at each node, including the corners of the scatterer. Due to the presence of an H-field singularity at the corner, there must be some treatment of the components placed there. To address this problem, images are introduced inside the cylinder to satisfy the boundary conditions and obtain nonzero H-field values on the corner. The results show good agreement with theory with the image corners, in place. The use of images for treatment of the singularity, while not giving the exact solution at the corner (which is not possible), gives very good surface current values which are quite close to the theoretical, a single grid point from the corner.<>