A Cylindrical Higher-Order FDTD Algorithm With PML and Quasi-PML

In this paper, we develop an higher-order finite-difference time-domain (HO-FDTD) scheme with a cylindrical grid for time-domain Maxwell's equations. The stability and dispersion property of the scheme is investigated and it is shown that larger cells decrease the numerical phase error, which makes it significantly lower than the finite-difference time-domain (FDTD) for low and medium discretizations, and the HO-FDTD scheme has an advantage of multiresolution time-domain (MRTD) in general. Moreover, two absorbing boundary conditions (ABCs) are derived for the cylindrical HO-FDTD grids. The first one is the PML based on stretched coordinates, and the other is the straightforward extension of Berenger's perfectly matched layer (PML) that is named quasi-PML (QPML) as it is no longer perfectly matched for cylindrical interfaces. The absorbing effectiveness of the two ABCs are compared and the numerical simulations validate that both PML schemes can provide a satisfactory absorbing boundary condition, while the QPML can save more computation time and computer memory.