Analysis and improvement of Liao ABC for FDTD

The finite-difference time-domain (FDTD) method is widely used for solving Maxwell´s equations in the time domain. FDTD is particularly good at dealing with small changes of the radio environment size in an inhomogeneous environment. One of the major issues in the usage of FDTD is the mesh truncation method. Liao´s absorbing boundary condition (ABC) is a widely used mesh truncation algorithm as it is valid for all incident angles and is implemented easily even in an inhomogeneous environment. The higher the order of Liao´s ABC, the higher its accuracy and its memory requirement. However, Liao´s ABC experiences instability. The paper considers the reduction of data storage requirements and enhancement of the stability.