Reflective boundary condition with arbitrary boundary shape for compact-explicit finite-difference time-domain method

Abstract

In this paper, we propose the reflective boundary condition with an arbitrary boundary shape for the compact-explicit finite-difference time-domain (CE-FDTD) method. The boundary condition with the arbitrary boundary shape is first formulated using an extension of the standard FDTD method. The boundary condition is then implemented into the CE-FDTD method in accordance with the position of the grid point. Some numerical demonstrations are given for sound reflection in a closed rectangular room and for sound diffraction by a rigid sphere to verify the validity of the proposed boundary condition. The numerical results are compared with the theoretical solutions. The validity of the proposed boundary condition with arbitrary boundary shape was confirmed through the numerical experiments.