A Cylindrical MRTD Algorithm With PML and Quasi-PML

In this paper, we develop an explicit multiresolution time-domain (MRTD) scheme based on Daubechies' scaling functions 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 finite difference time domain (FDTD) for low and medium discretizations, and the MRTD scheme has a slight advantage of high-order FDTD (2, 6). Moreover, two absorbing boundary conditions (ABCs) are derived for the cylindrical MRTD grids. The first one is the perfectly matched layer (PML) based on stretched coordinates, and the other is the straightforward extension of Berenger's PML, which is called the quasi perfectly matched layer (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 ABC, while the QPML can save more computation time and computer memory.