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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/3837 |
| Date | 16 August 2006 |
| Creators | Copeland, Dylan Matthew |
| Contributors | Pasciak, Joseph E. |
| Publisher | Texas A&M University |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | Book, Thesis, Electronic Dissertation, text |
| Format | 376087 bytes, electronic, application/pdf, born digital |
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