In this dissertation we are concerned with the analysis of the finite
element method for the time-dependent Maxwell interface problem when
Nedelec and Raviart-Thomas finite elements are employed and
preconditioning of the resulting linear system when implicit time schemes
are used.
We first investigate the finite element method proposed by Makridakis and
Monk in 1995. After studying the regularity of
the solution to time
dependent Maxwell's problem and providing approximation estimates for
the Fortin operator, we are able to give the optimal error estimate for the
semi-discrete scheme for Maxwell's equations.
Then we study preconditioners for linear systems arising in the finite
element method for time-dependent Maxwell's equations using implicit
time-stepping. Such linear systems are usually very large but sparse
and can only be solved iteratively. We consider overlapping Schwarz
methods and multigrid methods and extend some existing theoretical
convergence results. For overlapping Schwarz methods, we provide numerical
experiments to confirm the theoretical analysis.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/582 |
| Date | 30 September 2004 |
| Creators | Zhao, Jun |
| 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 | 394829 bytes, 103284 bytes, electronic, application/pdf, text/plain, born digital |
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