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Full-Text Articles in Physical Sciences and Mathematics
Uncertainty Quantification For Maxwell's Equations, Zhiwei Fang
Uncertainty Quantification For Maxwell's Equations, Zhiwei Fang
UNLV Theses, Dissertations, Professional Papers, and Capstones
This dissertation study three different approaches for stochastic electromagnetic fields based on the time domain Maxwell's equations and Drude's model: stochastic Galerkin method, stochastic collocation method, and Monte Carlo class methods. For each method, we study its regularity, stability, and convergence rates. Numerical experiments have been presented to verify our theoretical results. For stochastic collocation method, we also simulate the backward wave propagation in metamaterial phenomenon. It turns out that the stochastic Galerkin method admits the best accuracy property but hugest computational workload as the resultant PDEs system is usually coupled. The Monte Carlo class methods are easy to implement …
Arbitrary High Order Finite Difference Methods With Applications To Wave Propagation Modeled By Maxwell's Equations, Min Chen
UNLV Theses, Dissertations, Professional Papers, and Capstones
This dissertation investigates two different mathematical models based on the time-domain Maxwell's equations: the Drude model for metamaterials and an equivalent Berenger's perfectly matched layer (PML) model. We develop both an explicit high order finite difference scheme and a compact implicit scheme to solve both models. We develop a systematic technique to prove stability and error estimate for both schemes. Extensive numerical results supporting our analysis are presented. To our best knowledge, our convergence theory and stability results are novel and provide the first error estimate for the high-order finite difference methods for Maxwell's equations.