Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T07:26:34.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Boundary integral equations for the scattering of electromagnetic waves by a homogeneous dielectric obstacle

Published online by Cambridge University Press:  14 November 2011

P. A. Martin  and
Petri Ola
P. A. Martin
Affiliation:
Department of Mathematics, University of Manchester, Manchester M13 9PL, England, U.K.
Petri Ola
Affiliation:
Department of Mathematics, University of Helsinki, 00100 Helsinki, Finland
Get access Rights & Permissions [Opens in a new window]

Synopsis

Time-harmonic electromagnetic waves are scattered by a homogeneous dielectric obstacle. The corresponding electromagnetic transmission problem is reduced to a single integral equation over S for a single unknown tangential vector field, where S is the interface between the obstacle and the surrounding medium. In fact, several different integral equations are derived and analysed, including two previously-known equations due to E. Marx and J. R. Mautz, and two new singular integral equations. Mautz's equation is shown to be uniquely solvable at all frequencies. A new uniquely solvable singular integral equation is also found. The paper also includes a review of methods using pairs of coupled integral equations over S. It is these methods that are usually used in practice, although single integral equations seem to offer some computational advantages.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 1 , 1993 , pp. 185 - 208
Copyright
Copyright © Royal Society of Edinburgh 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Arvas, E. and Mautz, J. R.. On the non-uniqueness of the surface EFIE applied to multiple conducting and/or dielectric bodies. Archiv für Elektronik und Übertragungstechnik 42 (1988), 364–369.Google Scholar
2Colton, D. and Kress, R.. Integral Equation Methods in Scattering Theory (New York: Wiley, 1983).Google Scholar
3Colton, D. and Kress, R.. Time harmonic electromagnetic waves in an inhomogeneous medium. Proc. Roy. Soc. Edinburgh Sect. A 116 (1990), 279–293.CrossRefGoogle Scholar
4Costabel, M. and Stephan, E. P.. Strongly elliptic boundary integral equations for electromagnetic transmission problems. Proc. Roy. Soc. Edinburgh Sect. A 109 (1988), 271–296.CrossRefGoogle Scholar
5Glisson, A. W.. An integral equation for electromagnetic scattering from homogeneous dielectric bodies. IEEE Trans. Antennas and Propagation AP–32 (1984), 173–175.CrossRefGoogle Scholar
6Harrington, R. F.. Boundary integral formulations for homogeneous material bodies. J. Electromagnetic Waves and Applications 3 (1989), 1–15.CrossRefGoogle Scholar
7Jones, D. S.. Methods in Electromagnetic Wave Propagation (Oxford: Clarendon Press, 1979).Google Scholar
8Jost, G.. Integral equations with modified fundamental solution in time-harmonic electromagnetic scattering. IMA J. Appl. Math. 40 (1988), 129–143.CrossRefGoogle Scholar
9Kirsch, A.. Surface gradients and continuity properties for some integral operators in classical scattering theory. Math. Meth. Appl. Sci. 11 (1989), 789–804.CrossRefGoogle Scholar
10Kleinman, R. E. and Martin, P. A.. On single integral equations for the transmission problem of acoustics. SIAM J. Appl. Math. 48 (1988), 307–325.CrossRefGoogle Scholar
11Kress, R.. On boundary integral equation methods in stationary electromagnetic reflection. Lecture Notes in Mathematics 846 (1981), 210–226.CrossRefGoogle Scholar
12Kress, R.. On the boundary operator in electromagnetic scattering. Proc. Roy. Soc. Edinburgh Sect. A 103 (1986), 91–98.CrossRefGoogle Scholar
13Martin, P. A.. Identification of irregular frequencies in simple direct integral-equation methods for scattering by homogeneous inclusions. Wave Motion 13 (1991), 185–192.CrossRefGoogle Scholar
14Marx, E.. Single integral equation for wave scattering. J. Math. Phys. 23 (1982), 1057–1065.CrossRefGoogle Scholar
15Marx, E.. Integral equation for scattering by a dielectric. IEEE Trans. Antennas and Propagation AP–32 (1984), 166–172.CrossRefGoogle Scholar
16Mautz, J. R.. A stable integral equation for electromagnetic scattering from homogeneous dielectric bodies. IEEE Trans. Antennas and Propagation AP-37 (1989), 1070–1071.CrossRefGoogle Scholar
17Mautz, J. R. and Harrington, R. F.. Electromagnetic scattering from a homogeneous material body of revolution. Archiv für Elektronik und Übertragungstechnik 33 (1979), 71–80.Google Scholar
18Mautz, J. R. and Harrington, R. F., A combined-source solution for radiation and scattering from a perfectly conducting body. IEEE Trans. Antennas and Propagation AP-27 (1979), 445–454.CrossRefGoogle Scholar
19Müller, C.. Foundations of the Mathematical Theory of Electromagnetic Waves (Berlin: Springer, 1969).CrossRefGoogle Scholar
20Neave, G.. A uniquely solvable integral eqùation for the exterior electromagnetic scattering problem. Quart. J. Mech. Appl. Math. 40 (1987), 57–70.CrossRefGoogle Scholar
21Roach, G. F.. On the commutative properties of boundary integral operators. Proc. Amer. Math. Soc. 73 (1979), 219–227.CrossRefGoogle Scholar
22Shubin, M. A.. Pseudodifferential Operators and Spectral Theory (Berlin: Springer, 1987).CrossRefGoogle Scholar
23Stephan, E. P.. Boundary integral equations for magnetic screens in R 3. Proc. Roy. Soc. Edinburgh Sect. A 102 (1986), 189–210.CrossRefGoogle Scholar
24Taylor, M.. Pseudodifferential Operators (Princeton: University Press, 1981).CrossRefGoogle Scholar