Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-24T05:35:00.321Z Has data issue: false hasContentIssue false
  • English
  • Français

On the low frequency asymptotics for the 2-D electromagnetic transmission problem

Published online by Cambridge University Press:  17 February 2009

C. N. Anestopoulos  and
E. E. Argyropoulos
C. N. Anestopoulos
Affiliation:
National Technical University of Athens, Department of Applied Mathematics and Physics, GR-15780 Zografou Campus, Athens, Greece; e-mail: kanesto@mail.ntua.gr.
E. E. Argyropoulos
Affiliation:
Technological Education Institute, Department of Electrical Engineering, GR-35100 Lamia, Greece; e-mail: protepkste@stellad.pde.sch.gr.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We examine the transmission problem in a two-dimensional domain, which consists of two different homogeneous media. We use boundary integral equation methods on the Maxwell equations governing the two media and we study the behaviour of the solution as the two different wave numbers tend to zero. We prove that as the boundary data of the general transmission problem converge uniformly to the boundary data of the corresponding electrostatic transmission problem, the general solution converges uniformly to the electrostatic one, provided we consider compact subsets of the domains.

Type
Research Article
Information
The ANZIAM Journal , Volume 47 , Issue 3 , January 2006 , pp. 397 - 411
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Argyropoulos, E., “The transmission problem for the Helmholtz equation and the low wave number behavior of solution in two dimensions”, to appear.Google Scholar
[2]Argyropoulos, E. and Anestopoulos, C., “Low frequency asymptotics for the two-dimensional exterior electromagnetic problem”, Bull. Greek Math. Soc. 52 (2006).Google Scholar
[3]Chandler-Wilde, S. and Zhang, B., “A uniqueness result for scattering by infinite rough surfaces”, SIAM J. Appl. Math. 58 (1998) 1774–1790.CrossRefGoogle Scholar
[4]Colton, D. and Kress, R., Integral equations methods in scattering theory (John Wiley, New York, 1983).Google Scholar
[5]Dassios, G. and Kleinman, R., Low frequency scattering (Clarendon Press, Oxford, 2000).Google Scholar
[6]Kress, R., “On the low wave number asymptotics for the two-dimensional exterior Dirichlet problem for the reduced wave equation”, Math. Methods Appl. Sci. 9 (1987) 335–341.Google Scholar
[7]Kress, R. and Roach, G.F., “Transmission problems for the Helmholtz equation”, J. Mathematical Phys. 19 (1978) 1433–1437.CrossRefGoogle Scholar
[8]Torres, R. H., “A transmission problem in the scattering of electromagnetic waves by penetrable object”, SIAM J. Appl. Math. 27 (1996) 1406–1423.CrossRefGoogle Scholar
[9]Werner, P., “Low-frequency asymptotics for the reduced wave equation in two-dimensional exterior spaces”, Math. Methods Appl. Sci. 8 (1986) 134–156.CrossRefGoogle Scholar
[10]Wilde, P., “Transmission problems for the vector Helmholtz equation”, Proc. Roy. Soc. Edinburgh 105A (1987) 61–76.Google Scholar