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  • Compatible Discretizations for Maxwell's Equations with General Constitutive Laws

    Creator:
    McGregor, D. A.
    Abstract:
    In this thesis we construct compatible discretizations of Maxwell's equations. We use the term compatible to describe numerical methods for Maxwell's equations which obey many properties of vector Calculus in a discrete setting. Compatible discretizations preserve the exterior Calculus ensuring that the divergence of the curl and the curl of...
    Resource Type:
    Dissertation
    Full Text:
    ’ Law and Continuity Equation . . . . . . . . . . . . . . . . . . . 96 4.4 Numerical Demonstration of

  • Killing spinors and affine symmetry tensors in Gödel's Universe

    Creator:
    Cook, Samuel A.
    Abstract:
    The existence of generalized symmetries of Maxwell's equations in Gödel's Universe is investigated. It is shown that their existence is in turn tied to the existence of certain spinorial objects called Killing spinors. The conformal algebra, corresponding to valence (1; 1) Killing spinors, for Gödel's Universe is discussed in detail....
    Resource Type:
    Dissertation
    Full Text:
    Maxwell’s equations in Gödel’s Universe, a cosmological solution of Einstein’s equation. Due to the

  • Operator splitting methods for Maxwell's equations in dispersive media

    Creator:
    Keefer, Olivia A.
    Abstract:
    Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive...
    Resource Type:
    Masters Thesis
    Full Text:
    electromagnetic field. The combination of the Debye model and Maxwell’s equations, the Maxwell-Debye model, will

  • Time domain simulation of Maxwell's equations by the method of characteristics

    Creator:
    Orhanovic, Neven
    Abstract:
    A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the...
    Resource Type:
    Dissertation
    Full Text:
    Differential Equation Theory 17 2.1 Introductory Remarks on Partial Differential Equations 17 2.2 First