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Numerical Modeling of Electromagnetic Wave Scattering by Layered Random Surfaces




Ulmer, Kelsey

Type of Degree

PhD Dissertation


Mathematics and Statistics


We present an efficient numerical method for modeling the scattering of electromagnetic fields by a multiply layered medium with random interfaces. We propose a combination of the Monte Carlo-Transformed Field Expansion (MCTFE) Method with the use of Impedance-Impedance Operators to formulate the boundary conditions between the inner layers. The utilization of Impedance-Impedance Operators avoids singularities that typically arise in the inner layers when implementing the more frequently used Dirichlet to Neumann Operators. The primary components of the MCTFE Method are a domain flattening change of variables, a high order perturbation of surfaces expansion of the solutions, and Monte Carlo sampling. By using this method, the discretized differential operator will be the same for every Monte Carlo sample and for each perturbation order. This allows for an LU decomposition of the differential operator, which can then be called upon to solve the boundary value problem in each layer via backward and forward substitution. This leads to greatly reduced computational costs. The Karhunen-Loeve Expansion will be used to represent the random interfaces that separate each layer. After implementing the domain flattening change of variables and expanding the solutions as a Taylor series, the electromagnetic fields will be approximated using the Chebyshev polynomials, so that we can express the differential operator using Chebyshev differentiation matrices and solve the boundary value problems via collocation. Numerical results will be presented to demonstrate the accuracy of the method.