Particle Methods for Electromagnetic Wave Propagation Problems.

摘要

1. A rigorous proof of the relation between the solutions of wave and telegraph equations in 3D via a random 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.