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Finite Element Methods for Maxwell's Equations$
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Peter Monk

Print publication date: 2003

Print ISBN-13: 9780198508885

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198508885.001.0001

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Algorithmic Development

Algorithmic Development

Chapter:
(p.332) 13 Algorithmic Development
Source:
Finite Element Methods for Maxwell's Equations
Author(s):

Peter Monk

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198508885.003.0013

This chapter examines the phase error problem and also shows, via a dispersion analysis, that higher order methods can significantly improve phase accuracy. Once a solution is computed it is desirable to assess the accuracy of the solution to determine how to refine the mesh. The next section of the chapter presents a residual based a posteriori error analysis that shows how both the error in the curl of the solution and the divergence needs to be assessed. The final section concerns absorbing boundary conditions, which are often used in preference to the ‘exact’ techniques in Chapters 10-12 to ease the implementation burden. The standard Silver-Muller condition, infinite elements, and the justly popular Perfectly Matched Layer (PML) of Berenger are discussed.

Keywords:   Schwarz method, iterative scheme, phase error, dispersion, a posteriori error, residual, absorbing boundary condition, perfectly matched layer

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