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

Many applications require time-domain solutions of Maxwell's equations in i nhomogeneous, conductive media involving cylindrical geometries with both e lectrically small and large structures. The conventional finite-difference time-domain (FDTD) method with a uniform Cartesian grid will result in a st aircasing error, and wastes many unnecessary cells in regions with large st ructures 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 equati ons. A refined lattice is used near sharp edges and within fine geometrical details, while a larger lattice is used outside these regions. This provid es an efficient use of limited computer memory and computation time. We use two absorbing boundary conditions to a nonuniform cylindrical grid: 1) the straightforward extension of Berenger's perfectly matched lager (PR;IL) wh ich is no longer perfectly matched for cylindrical interfaces, thus the nam e 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 bounda ry conditions (ABC's and to demonstrate the effectiveness of the nonuniform grid and the absorbing boundary conditions.