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On boundary integral equation methods in stationary electromagnetic reflection

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Book cover Ordinary and Partial Differential Equations

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 846))

Abstract

Analogously to the methods proposed by Brakhage, Werner, Leis, Panich, Burton and Miller for exterior boundary-value problems for the scalar Helmholtz equation (this means for boundary-value problems from acoustic reflection), exterior boundary-value problems from the mathematical theory of electromagnetic reflection at perfect conductors are reduced to integral equations which are uniquely solvable for all frequencies. These integral equations are singular and require certain regularization techniques.

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References

  1. Brakhage, H. and Werner, P.: Über das Dirichletsche Außenraumproblem für die Helmholtzsche Schwingungsgleichung. Arch. Math. 16 (1965), 325–329.

    Article  MathSciNet  MATH  Google Scholar 

  2. Burton, A.J. and Miller, G.F.: The application of integral equation methods to the numerical solution of some exterior boundary-value problems. Proc. R. Soc. A 323 (1971), 201–210.

    Article  MathSciNet  MATH  Google Scholar 

  3. Greenspan, D. and Werner, P.: A numerical method for the exterior Dirichlet problem for the reduced wave equation. Arch. Rat. Mech. Anal. 23 (1966), 288–316.

    Article  MathSciNet  MATH  Google Scholar 

  4. Jones, D.S.: Integral equations for the exterior acoustic problem. Quart. J. Mech. Appl. Math. 27 (1974), 129–142.

    Article  MathSciNet  MATH  Google Scholar 

  5. Knauff, W.: Ein numerisches Verfahren zur Lösung eines Außenraumproblems für die vektorielle Helmholtzgleichung. To appear.

    Google Scholar 

  6. Knauff, W. and Kress, R.: On the exterior boundary-value problem for the time-harmonic Maxwell equations. J. Math. Anal. Appl. 72 (1979), 215–235.

    Article  MathSciNet  MATH  Google Scholar 

  7. Knauff, W. and Kress, R.: A modified integral equation method for the electric boundary-value problem for the vector Helmholtz equation. To appear in ISNM.

    Google Scholar 

  8. Kress, R.: On the existence of a solution to a singular integral equation in electromagnetic reflection. To appear in J. Math. Anal. Appl.

    Google Scholar 

  9. Kupradse, W.D.: Randwertaufgaben der Schwingungstheorie und Integralgleichungen. Berlin, VEB Deutscher Verlag der Wissenschaften 1956.

    MATH  Google Scholar 

  10. Kussmaul, R.: Ein numerisches Verfahren zur Lösung des Neumannschen Außenraumproblems für die Helmholtzsche Schwingungsgleichung. Computing 4 (1969), 246–273.

    Article  MathSciNet  MATH  Google Scholar 

  11. Leis, R.: Zur Dirichletschen Randwertaufgabe des Außenraumes der Schwingungsgleichung. Math. Z. 90 (1965), 205–211.

    Article  MathSciNet  MATH  Google Scholar 

  12. Leis, R.: Vorlesungen über partielle Differentialgleichungen zweiter Ordnung. Mannheim, Bibliographisches Institut 1967.

    MATH  Google Scholar 

  13. Mautz, J.R. and Harrington, R.F.: H-field, E-field, and combined-field solutions for conducting bodies of revolution. Archiv f. Elektronik u. Übertragungstechnik 32 (1978), 159–164.

    Google Scholar 

  14. Mautz, J.R. and Harrington, R.F.: A combined-source solution for radiation and scattering from a perfectly conduction body. IEEE Trans. Antennas Propagat. AP-27 (1979), 445–454.

    Article  Google Scholar 

  15. Müller, C.: Über die Beugung elektromagnetischer Schwingungen an endlichen homogenen Körpern. Math. Ann. 123 (1951), 345–378.

    Article  MathSciNet  MATH  Google Scholar 

  16. Müller, C.: Randwertprobleme der Theorie elektromagnetischer Schwingungen. Math. Z. 56 (1952), 261–270.

    Article  MathSciNet  MATH  Google Scholar 

  17. Müller, C.: Grundprobleme der mathematischen Theorie elektromagnetischer Schwingungen. Berlin-Göttingen-Heidelberg, Springer 1957.

    Book  MATH  Google Scholar 

  18. Müller, C. and Niemeyer, H.: Greensche Tensoren und asymptotische Gesetze der elektromagnetischen Hohlraumschwingungen. Arch. Rat. Mech. Anal. 7 (1961), 305–348.

    Article  MathSciNet  MATH  Google Scholar 

  19. Panich, O.I.: On the question of the solvability of the exterior boundary-value problems for the wave equation and Maxwell's equations. Russ. Math. Surv. 20 (1965), 221–226.

    Google Scholar 

  20. Ursell, F.: On the exterior problems of acoustic. Proc. Cambridge Philos. Soc. 74 (1973), 117–125.

    Article  MathSciNet  MATH  Google Scholar 

  21. Ursell, F.: On the exterior problems of acoustics. Proc. Cambridge Philos. Soc. 84 (1978) 545–548.

    Article  MathSciNet  MATH  Google Scholar 

  22. Werner, P.: On the exterior boundary-value problem of perfect reflection for stationary electromagnetic wave fields. J. Math. Anal. Appl. 7 (1963), 348–396.

    Article  MathSciNet  MATH  Google Scholar 

  23. Werner, P.: On the behavior of stationary electromagnetic wave fields for small frequencies. J. Math. Anal. Appl. 15 (1966), 447–496.

    Article  Google Scholar 

  24. Werner, P.: Über das Verhalten elektromagnetischer Felder für kleine Frequenzen in mehrfach zusammenhängenden Gebieten. J. f. d. reine u. angew. Math. I, 278/279 (1975), 365–397; II, 280 (1976), 98–121.

    MATH  Google Scholar 

  25. Weyl, H.: Die natürlichen Randwertaufgaben im Außenraum für Strahlungsfelder beliebiger Dimension und beliebigen Ranges. Math. Z. 56 (1952), 105–119.

    Article  MathSciNet  MATH  Google Scholar 

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Authors
  1. Rainer Kress
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W. N. Everitt B. D. Sleeman

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© 1981 Springer-Verlag

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Kress, R. (1981). On boundary integral equation methods in stationary electromagnetic reflection. In: Everitt, W.N., Sleeman, B.D. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 846. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0089839

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  • DOI: https://doi.org/10.1007/BFb0089839

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10569-5

  • Online ISBN: 978-3-540-38538-7

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