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Divergence boundary conditions for vector Helmholtz equations withdivergence constraints

Published online by Cambridge University Press:  15 August 2002

Urve Kangro  and
Roy Nicolaides
Urve Kangro
Affiliation:
Department of Mathematics, Tartu University, Tartu, Estonia. ukangro@ut.ee.
Roy Nicolaides
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. The work of this author was supported by the United States Air Force Office of Scientific Research under grants F-49620-94-1-0311 and F-49620-97-1-0204.
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Abstract

The idea of replacing a divergence constraint by a divergence boundarycondition is investigated. The connections between the formulations areconsidered in detail. It is shown that the most common methods of usingdivergence boundary conditions do not always work properly. Necessaryand sufficient conditions for the equivalence of the formulations aregiven.

Keywords

Maxwell's equationsdivergence boundary conditionsHelmholtz equationdivergence constraints.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 3 , May 1999 , pp. 479 - 492
Copyright
© EDP Sciences, SMAI, 1999

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