Advances in the perfectly matched layer absorbing boundary condition and a technique for efficiently modeling long path propagation with applications to finite-difference grid techniques

The Perfectly Matched Layer (PML) absorbing boundary condition was introduced by Berenger (1993) and Chew and Weedon (1994) as a means for truncating Finite-Difference Time-Domain (FDTD) and Finite-Difference Frequency Domain (FDFD) lattices in order to accurately simulate electromagnetic antenna and scattering problems in isotropic media. In the ionosphere and magnetosphere, where the dominant medium is a magnetized plasma, numerous interesting electromagnetic wave phenomena occur. Many of these would be well suited for analysis by the FDTD and/or FDFD methods, however, until recent developments, including contributions in this dissertation, the PML had not been efficiently extended nor capable, in some cases, to truncate domains containing magnetized plasma. In this dissertation, we develop two methods for extending Chew's formulation to robustly and efficiently truncate any linear magnetized plasma as well as any linear media.; A method for calculating the numerical reflection coefficient for the PMLs introduced in this dissertation is developed for general linear media. The derived expressions for the numerical reflection coefficient are used to quantify the performance of the PML for incident plane waves at any incident angle, frequency and polarization. Two and three dimensional numerical test results, which validate the calculation of the numerical reflection coefficient, are presented. For the case of the PML truncating free space, values of up to -100 dB for the numerical reflection coefficient are realized. For the case of the PML truncating a magnetized plasma, values from -40 dB up to -90 dB are realized, depending on the orientation of the ambient magnetic field with respect to the PML.; Finally, a technique is developed for the efficient modeling of propagation over long paths (hundreds of wavelengths) by breaking the path up into segments and appropriately applying the PML and total-field/scattered-field method. For FDTD simulations the new technique is well suited to model both slow and fast wave modes as well as scattering inhomogeneities along the path. In addition, the new technique is directly applicable to FDFD simulations. Both FDTD and FDFD numerical simulations of propagation within the Earth-ionosphere waveguide are performed to validate the new technique.