A nonuniform cylindrical FDTD algorithm with improved PML and quasi-PML absorbing boundary conditions

Abstract

Many applications require time-domain solutions of Maxwell's equations in inhomogeneous, conductive media involving cylindrical geometries with both electrically small and large structures. The conventional finite-difference time-domain (FDTD) method with a uniform Cartesian grid will result in a staircasing error, and wastes many unnecessary cells in regions with large structures in order to accommodate the accurate geometrical representation in regions with small structures. In this work, an explicit FDTD method with a nonuniform cylindrical grid is developed for time-domain Maxwell's equations. A refined lattice is used near sharp edges and within fine geometrical details, while a larger lattice is used outside these regions. This provides an efficient use of limited computer memory and computation time. The authors use two absorbing boundary conditions to a nonuniform cylindrical grid: (1) the straightforward extension of Berenger's perfectly matched layer (PML) which is no longer perfectly matched for cylindrical interfaces, thus the name quasi-PML, (QPML); (2) the improved true PML based on complex coordinates. In practice, both PML schemes can provide a satisfactory absorbing boundary condition. Numerical results are shown to compare the two absorbing boundary conditions (ABCs) and to demonstrate the effectiveness of the nonuniform grid and the absorbing boundary conditions.