A Fredholm integral equation approach to propagation over irregular terrain

A method based on the Fredholm-type integral equation is presented to predict propagation of electromagnetic fields due to a two dimensional source. The method is efficient precisely where the Volterra equation approach fails, and in this sense complements it. The transmitting antenna is vertically polarized and is assumed to generate two-dimensional waves. Propagation is described by terrain elevation profile and the local surface impedance which may vary with distance. The domain of interest is made finite by enclosing the source and the terrain irregularities inside a semicircular boundary on which Bayliss-Turkel radiation boundary conditions are applied to simulate free-space. A boundary integral equation consisting of the irregular terrain and the outer boundary is formulated and solved by the boundary-element method. Numerical results are presented.<>