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A Polynomial Chaos Method for Dispersive Electromagnetics

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Probabilistic methods, simulation and stochastic differential equations Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  23 November 2015

Nathan L. Gibson
Nathan L. Gibson*
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, OR 97331, USA.
*
*Corresponding author. Email address: gibsonn@math.oregonstate.edu (N. L. Gibson)
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Abstract

Electromagnetic wave propagation in complex dispersive media is governed by the time dependent Maxwell's equations coupled to equations that describe the evolution of the induced macroscopic polarization. We consider “polydispersive” materials represented by distributions of dielectric parameters in a polarization model. The work focuses on a novel computational framework for such problems involving Polynomial Chaos Expansions as a method to improve the modeling accuracy of the Debye model and allow for easy simulation using the Finite Difference Time Domain (FDTD) method. Stability and dispersion analyzes are performed for the approach utilizing the second order Yee scheme in two spatial dimensions.

Keywords

Maxwell's equationsDebye polarizationrelaxation time distributionFDTD

MSC classification

Secondary: 35Q61: Maxwell equations 65C99: None of the above, but in this section 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 5 , November 2015 , pp. 1234 - 1263
Copyright
Copyright © Global-Science Press 2015 

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