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Negative-norm least-squares methods for axisymmetric Maxwell equations

We develop negative-norm least-squares methods to solve the three-dimensional
Maxwell equations for static and time-harmonic electromagnetic fields in the case of
axial symmetry. The methods compute solutions in a two-dimensional cross section
of the domain, thereby reducing the dimension of the problem from three to two. To
achieve this dimension reduction, we work with weighted spaces in cylindrical coordinates.
In this setting, approximation spaces consisting of low order finite element
functions and bubble functions are analyzed.
In contrast to other methods for axisymmetric Maxwell equations, our leastsquares
methods allow for discontinuous coefficients with large jumps and non-convex,
irregular polygonal domains discretized by unstructured meshes. The resulting linear
systems are of modest size, are symmetric positive definite, and can be solved very
efficiently. Computations demonstrate the robustness of the methods with respect to
the coefficients and domain shape.

Identiferoai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/3837
Date16 August 2006
CreatorsCopeland, Dylan Matthew
ContributorsPasciak, Joseph E.
PublisherTexas A&M University
Source SetsTexas A and M University
Languageen_US
Detected LanguageEnglish
TypeBook, Thesis, Electronic Dissertation, text
Format376087 bytes, electronic, application/pdf, born digital

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