Fast Algorithms for Long-Range Wave Propagation over Complex Terrain

Parabolic Wave Equations are an area of extensive research in the description of wave propagation. The Split-Step Fourier method solves the Parabolic Wave Equation spectrally and is a method of choice for long-range propagation through atmosphere. Split-Step Fourier methods, however, are unable to sparsely represent fields and require repeated forward and inverse Fourier Transforms. Furthermore, Radiation Boundary Conditions are cumbersome to implement due to the Periodic Boundary Conditions enforced by the spectral propagator. This thesis solves the one-way wave equation in 2D and 3D with Gabor Transforms, representing propagating fields as a sum of locally supported frame functions with spatial shifts and frequency modulations. Gabor Transforms easily exploit sparsity in the space-frequency representation of structured fields. Radiation Boundary Conditions are trivially implemented by removing frame functions that propagate outside the computational domain (i.e. beyond certain height bounds) from consideration, a feat that is impossible using classical split-step Fourier methods. Phase screens, formerly requiring immense computational resources to be applied in the spatial domain, are implemented in the Gabor domain. Terrain models are implemented by hybridizing fast atmospheric propagators with rigorous solvers for scattering from hills and forest.

 Chair: Professor Eric Michielssen