Resolution of Maxwell’s equations in a domain with a reentrant corner. (Résolution des équations de Maxwell dans un domaine avec un coin rentrant.) (French. Abridged English version) Zbl 0855.65131

Assous, Franck; Ciarlet, Patrick jun.; Sonnendrücker, Eric

C. R. Acad. Sci., Paris, Sér. I 323, No. 2, 203-208 (1996).

Summary: In the case when the computational domain has a reentrant corner, we give a decomposition of the solution of Maxwell’s equations into the sum of a regular part and a singular part, the singular part being the solution of a steady state problem. The exact regularity of the solution is given depending on the angle of the reentrant corner. The decomposition is then used to introduce an algorithm for the numerical resolution of Maxwell’s equations in presence of reentrant corners.

MSC:

65Z05	Applications to the sciences
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
35Q60	PDEs in connection with optics and electromagnetic theory
78A35	Motion of charged particles

Keywords:

reentrant corner; decomposition of the solution; Maxwell’s equations; regular part; singular part