Title :
Asymptotic expansion of the electromagnetic field in the vicinity of domain’s borders
Author_Institution :
Dept. of Differential Equations, Dnepropetrovsk Nat. Univ., Dnipropetrovsk
fDate :
June 29 2008-July 2 2008
Abstract :
The problem of construction the asymptotic expansion of an electromagnetic field in a vicinity of domainpsilas borders is considered. The solution of a problem is constructed as product of functions so that boundary conditions have been satisfied. In case of zero boundary conditions one of factors in the solution tends to zero on border and consequently near the border can be accepted as small parameter. The Helmholtz equation becomes singularly perturbed and it allows constructing the solution as a boundary layer. The asymptotic expansion is obtained in an explicit form for domains which borders consist on the various combinations of curves of a special kind. It is shown, that asymptotic expansion of the solution is continuous in all a boundary layer.
Keywords :
Helmholtz equations; boundary layers; differential equations; electric domains; electromagnetic field theory; magnetic domains; perturbation techniques; Helmholtz equation; asymptotic expansion; boundary layer; domain borders; electromagnetic field; explicit form; singularly perturbed differential equations; zero boundary conditions; Boundary conditions; Differential equations; Electromagnetic fields; Electromagnetic radiation; Electromagnetic reflection; Electromagnetic refraction; Electromagnetic scattering; Geometry; Surface waves;
Conference_Titel :
Mathematical Methods in Electromagnetic Theory, 2008. MMET 2008. 12th International Conference on
Conference_Location :
Odesa
Print_ISBN :
978-1-4244-2284-5
DOI :
10.1109/MMET.2008.4580924