Characterization of the singular part of the solution of Maxwell's equations in a polyhedral domain

F. Assous; P. Ciarlet; P. A. Raviart; E. Sonnendrücker

doi:10.1002/(SICI)1099-1476(199904)22:6<485::AID-MMA46>3.0.CO;2-E

Characterization of the singular part of the solution of Maxwell's equations in a polyhedral domain

F. Assous, P. Ciarlet, P. A. Raviart, E. Sonnendrücker

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27 Scopus citations

Abstract

The solution of Maxwell's equations in a non-convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian.

Original language	English
Pages (from-to)	485-499
Number of pages	15
Journal	Mathematical Methods in the Applied Sciences
Volume	22
Issue number	6
DOIs	https://doi.org/10.1002/(SICI)1099-1476(199904)22:6<485::AID-MMA46>3.0.CO;2-E
State	Published - Apr 1999
Externally published	Yes

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10.1002/(SICI)1099-1476(199904)22:6<485::AID-MMA46>3.0.CO;2-E

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abstract = "The solution of Maxwell's equations in a non-convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian.",

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N2 - The solution of Maxwell's equations in a non-convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian.

AB - The solution of Maxwell's equations in a non-convex polyhedral domain is less regular than in a smooth or convex polyhedral domain. In this paper we show that this solution can be decomposed into the orthogonal sum of a singular part and a regular part, and we give a characterization of the singular part. We also prove that the decomposition is linked to the one associated to the scalar Laplacian.

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Characterization of the singular part of the solution of Maxwell's equations in a polyhedral domain

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