This paper is concerned with a point-oriented finite volume time domain (FVTD) method in the Cartesian coordinate system for analyzing electromagnetic wave scattering by arbitrary shaped metallic gratings. The perfectly matched layer (PML) is used for the absorbing boundary conditions (ABC's) in the directions corresponding to transmitted and reflected wave regions. An FVTD version of the Floquet's theorm is described to impose the periodic condition in the direction where conducting rods are located periodically. The boundary conditions for a conductor rod which is not well suited to the Cartesian coordinate system are satisfied in an average fashion by introducing image fields at image points. It is shown that the present method gives accurate numerical results. Numerical calculations are also carried out for thick conducting rods which seem difficult to deal with in an analytical way.

This paper is concerned with a point-oriented finite volume time domain (FVTD) method in the Cartesian coordinate system and its application to the analysis of electro-magnetic wave propagation in a bended waveguide as well as radiation from and receiving by a horn antenna with a flange of arbitrary angle. The perfectly matched layer (PML) is used for the absorbing boundary conditions (ABC's). The boundary conditions for a perfect conductor not well suited to the Cartesian coordinate system are also proposed. According to this algorithm, the boundary conditions are satisfied in an average fashion at the conductor surface without changing the computational scheme. In this sense, numerical computations based on the present method are simple but flexible. Numerical results show good convergence.