Browsing by Author "Bunting, Charles Frederick"

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    Functionals in electromagnetics: an investigation into methods to eliminate spurious solutions in the application of finite element techniques
    Bunting, Charles Frederick (Virginia Tech, 1994-07-12)
    Finite element techniques have been applied to a wide variety of problems in electro magnetics, but have been handicapped by the appearance of spurious solutions. Both weighted residual methods and variational methods are the basic finite element techniques that are examined to establish a framework for the discussion of spurious solutions. A simple waveguide example is used to explore the fundamental problem with these spurious solutions. A method is developed that focuses on the functional form as the fundamental cause underlying the difficulties with spurious solutions. By using analytical rather than numerical means, it is shown that the solution form allows for the existence of an improper gradient behavior in a general field expansion. A new functional that satisfies Maxwell's equations and eliminates spurious solutions is introduced. This new functional is shown to be self-adjoint and positive definite, thus providing an error minimization. The analytical form as well as the finite element method is applied to demonstrate the robust nature of the functional.
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    Issues related to finite element techniques for two dimensional transmission structures
    Bunting, Charles Frederick (Virginia Tech, 1992-04-19)
    This thesis addresses many issues associated with finite element techniques, concentrating on ideas that are not often emphasized in the literature. Pulling together the ideas of mesh generation, sparse storage solution techniques, and functional development, in a single volume, this work provides basic tools for implementation of finite element techniques for both static and dynamic problems in electromagnetics. An automatic mesh generation scheme is developed by forming a Delaunay triangulation. A storage technique will be presented and used In conjunction with a conjugate gradient method to solve linear systems of equations. Application to electromagnetic problems will be demonstrated in the static, quasi-static, and full-field regimes. Laplace's equation is solved for various transmission line geometries to obtain capacitance and characteristic impedance. A finite element model that is a full field expression of Maxwell's equations is developed through a novel variational formulation involving the method of Lagrange multipliers, with attention given to the physical basis of the obtained functional. This model is then applied to the problem of determining the propagation constant of a waveguide.