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

Boniface Nkemzi (1)

1 CALVI - Scientific computation and visualization

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.

Mots clés: Maxwell's equations; singularities; Fourier method

Domaines: Equations aux dérivées partielles [math.AP]

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