# Asymptotic expansion of the solution of Maxwell's equations in polygonal plane domains

1 CALVI - Scientific computation and visualization
IRMA - Institut de Recherche Mathématique Avancée, LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection, Inria Nancy - Grand Est, IECL - Institut Élie Cartan de Lorraine
Abstract : This paper is mainly concerned with the structure of the singular and regular parts of the solution of time-harmonic Maxwell's equations in polygonal plane domains. The asymptotic behaviour of the solution near corner points of the domain is studied by means of discrete Fourier transformation. A detailed functional analysis of the solution shows that the boundary value problem does not belong locally to~$H^2$ when the boundary of the domain has non-acute angles, and explicit formulas for the singularity functions and their corresponding coefficients are given.
Keywords :
Document type :
Reports

Cited literature [31 references]

https://hal.inria.fr/inria-00000170
Contributor : Simon Labrunie <>
Submitted on : Tuesday, July 19, 2005 - 7:35:18 PM
Last modification on : Friday, June 19, 2020 - 9:22:04 AM
Long-term archiving on: : Thursday, April 1, 2010 - 10:04:50 PM

### Identifiers

• HAL Id : inria-00000170, version 1

### Citation

Boniface Nkemzi. Asymptotic expansion of the solution of Maxwell's equations in polygonal plane domains. [Research Report] 2005, pp.26. ⟨inria-00000170⟩

Record views