Numerical Modeling of the Parabolic Wave Equation in Lossless and Lossy Media

Abstract

Complexity of Electromagnetic (EM) problems often require numerical methods when an analytic solution is unattainable or at least impractical to obtain analytically. The type of numerical technique selected is often dictated by the domain of the problem to be solved and the allowable error in the computation of the solution. This paper focuses on the concept of applying numerical techniques to solve the parabolic wave equation in environments with domain variation. The numerical techniques considered are Finite Difference, Finite Element, and Spectral methods. Analysis of numerical error contributors and assessing stability regions of each method are discussed in conjunction with the calculation of each model's order of accuracy and computational complexity. Difficulties in the representation of the domain as it pertains to the numerical method applied is also addressed. The variation in the domain is enforced through the use of a Gaussian lens. A Gaussian lens is implemented in a composite form in order to create a system that is supportive of Multiple Phase Screen Theory application. Multiple Phase Screens will be implemented later in the research effort, to model the random nature of the plasmas encountered in the ionosphere.