Modeling the Diffraction of Electromagnetic Waves over Underwater Objects; the Wiener-Hopf Integral Equation
Yajni Warnapala *
Department of Mathematics, Roger Williams University, Bristol, RI USA.
Cole Foster
Department of Mathematics, Roger Williams University, Bristol, RI USA.
*Author to whom correspondence should be addressed.
Abstract
This research, inspired by the loss of Malaysian Airline Flight 370, investigates the feasibility of obtaining good convergence results for a model of the interaction of electromagnetic waves over the surface of the Spherical Biconcave Disc. The Galerkin Method is used to numerically solve the Dirichlet and Neumann exterior boundary value problems for the Wiener-Hopf Integral Equation over the half-plane of the Spherical Biconcave Disc. This modeling accounts for the attenuation losses of the propagating electromagnetic wave as a result of absorption and scattering in lossy media with comparison to lossless propagation. The numerical results of this research nds good convergence for this model as well as limitations in the transmission of electromagnetic waves underwater.
Keywords: Wiener-Hopf, galerkin, neumann, dirichlet, attenuation, lossless, lossy, plane-wave, propagation.