One-Step Leapfrog ADI-FDTD Method in 3-D Cylindrical Grids With a CPML Implementation

A three-dimensional (3-D) unconditionally stable one-step leapfrog alternating-direction-implicit finite-difference time-domain (ADI-FDTD) method in the cylindrical coordinate system is presented. It is more computationally efficient while preserving the properties of the two-step scheme. By reusing the auxiliary variable, it also uses less memory than the two-step scheme. In contrast with the one-step leapfrog ADI-FDTD method in the Cartesian coordinate system, some implicit equations of the one-step leapfrog ADI-FDTD method in the cylindrical coordinate system are not tridiagonal equations. The Sherman Morrison formula is used to solve them efficiently. To solve open region problems, convolutional perfectly matched layer (CPML) for the one-step leapfrog scheme is proposed. Numerical results are presented to validate them.