NF - 10 - 1 - 0305 413 - 545 - 0937 Final Report 57313

Particle Methods for Electromagnetic Wave Propagation Problems Report Title 1. A rigorous proof of the relation between the solutions of wave and telegraph equations in 3D via arandom time induced by a Poisson process has been provided using techniques of stochastic calculus. Application of this relation to wave propagation in dispersive media (Lorentz and Drude media) is discussed. 2. Sparse grid collocation methods that are used for uncertainty quantification have been applied to electromagnetic propagation problems. Two applications are considered--the first application involves waves propagating in dielectric media with uncertain permittivities and permeabilities, in which several cases with increasing random space dimensionality are exemplified. The objective in the second application is to compute expected signal strength above flat Earth surface at ranges far from transmitter location, where randomness is present due to uncertain refractive index of the atmosphere. The uncertainty is extracted from published measurements, and constitutes longterm variation. Two different sparse grid algorithms are demonstrated and the deterministic evaluators are accessed as a black box by the sparse grid algorithms. Strengths of the two algorithms are differentiated depending on the characteristics of the randomness. (a) Papers published in peer-reviewed journals (N/A for none) Enter List of papers submitted or published that acknowledge ARO support from the start of the project to the date of this printing. List the papers, including journal references, in the following categories: