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Volumn 24, Issue 5-6, 1999, Pages 24-38

Generalized impedance boundary conditions for the Maxwell equations as singular perturbations problems

Author keywords

Fredholm system; Generalized Impedance Boundary Conditions; Integral Equations; Maxwell's Equations; Singular Perturbation Problem; The Hodge decomposition Theorem

Indexed keywords


EID: 0033475011     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309908821448     Document Type: Article
Times cited : (19)

References (51)
  • 1
    • 0009225179 scopus 로고
    • On an exterior Laplace equation problem with Robin boundary condition
    • J.F. Ahner et H.W. Wiener. On an exterior Laplace equation problem with Robin boundary condition. J. Math. Anal. Appl., 157 (1991), 127-146.
    • (1991) J. Math. Anal. Appl. , vol.157 , pp. 127-146
    • Ahner, J.F.1    Wiener, H.W.2
  • 2
    • 0032099379 scopus 로고    scopus 로고
    • Low frequency behavior of solutions to electromagnetic scattering problems in chiral media
    • H. Ammari, M. Laouadi and J.C. Nédélec. Low frequency behavior of solutions to electromagnetic scattering problems in chiral media. SIAM J. Appl. Math., 58 (3) (1998), 1022-1042.
    • (1998) SIAM J. Appl. Math. , vol.58 , Issue.3 , pp. 1022-1042
    • Ammari, H.1    Laouadi, M.2    Nédélec, J.C.3
  • 4
    • 0009224418 scopus 로고    scopus 로고
    • Équation intégrale et diffraction dans un milieu chiral
    • H. Ammari and J.C. Nédélec. Équation intégrale et diffraction dans un milieu chiral. C. R. Acad. Sci. Paris. Série I, 322 (1996), 1087-1091.
    • (1996) C. R. Acad. Sci. Paris. Série I , vol.322 , pp. 1087-1091
    • Ammari, H.1    Nédélec, J.C.2
  • 5
    • 0040757667 scopus 로고    scopus 로고
    • Time-harmonic electromagnetic fields in thin chiral curved layers
    • H. Ammari and J.C. Nédélec. Time-harmonic electromagnetic fields in thin chiral curved layers. SIAM J. Math. Anal., 29 (2) (1998), 395-423.
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.2 , pp. 395-423
    • Ammari, H.1    Nédélec, J.C.2
  • 6
    • 0025539718 scopus 로고
    • The resistive and conductive problems for the exterior Heimholtz equation
    • T.S. Angell, R.E. Kleinman and F. Hettlich. The resistive and conductive problems for the exterior Heimholtz equation. SIAM J. Appl. Math., 50 (6) (1990), 1607-1622.
    • (1990) SIAM J. Appl. Math. , vol.50 , Issue.6 , pp. 1607-1622
    • Angell, T.S.1    Kleinman, R.E.2    Hettlich, F.3
  • 7
    • 0027097379 scopus 로고
    • The conductive boundary condition for Maxwell's equations
    • T.S. Angell and A. Kirsch. The conductive boundary condition for Maxwell's equations. SIAM J. Appl. Math., 52 (6) (1992), 1597-1610.
    • (1992) SIAM J. Appl. Math. , vol.52 , Issue.6 , pp. 1597-1610
    • Angell, T.S.1    Kirsch, A.2
  • 8
    • 84966239375 scopus 로고
    • Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element. Part I: The continuous problem
    • A. Bendali. Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element. Part I: the continuous problem. Math. Comp., 43 (1984), 29-46.
    • (1984) Math. Comp. , vol.43 , pp. 29-46
    • Bendali, A.1
  • 9
    • 0030398896 scopus 로고    scopus 로고
    • The effect of a thin coating on the scattering of a time-harmonic wave for the Heimholtz equation
    • A. Bendali and K. Leimabet. The effect of a thin coating on the scattering of a time-harmonic wave for the Heimholtz equation. SIAM J. Appl. Math., 56 (6) (1996), 1664-1693.
    • (1996) SIAM J. Appl. Math. , vol.56 , Issue.6 , pp. 1664-1693
    • Bendali, A.1    Leimabet, K.2
  • 10
    • 0009292493 scopus 로고
    • Résolution par éléments finis de frontière d'un problème de diffraction d'onde comportant une condition aux limites d'impédance généralisées
    • A. Bendali and L. Vernhet. Résolution par éléments finis de frontière d'un problème de diffraction d'onde comportant une condition aux limites d'impédance généralisées, C. R. Acad. Sci., Paris. Série I, 321 (1995), 791-797.
    • (1995) C. R. Acad. Sci., Paris. Série I , vol.321 , pp. 791-797
    • Bendali, A.1    Vernhet, L.2
  • 11
    • 0011632768 scopus 로고
    • Méthodes asymptotiques en electromagnétisme
    • Springer Verlag
    • D. Bouche and F. Molinet. Méthodes asymptotiques en electromagnétisme. Mathématiques et Applications 16, Springer Verlag (1994).
    • (1994) Mathématiques et Applications , vol.16
    • Bouche, D.1    Molinet, F.2
  • 12
    • 0009154468 scopus 로고
    • The multipole expansion of radiation fields
    • A. P. Calderòn, The multipole expansion of radiation fields, J. Rational Mech. Anal., 3 (1954), 523-537.
    • (1954) J. Rational Mech. Anal. , vol.3 , pp. 523-537
    • Calderòn, A.P.1
  • 13
    • 0019686122 scopus 로고
    • The impedance boundary value problem for the time-harmonic Maxwell equations
    • D. Colton and R. Kress, The impedance boundary value problem for the time-harmonic Maxwell equations. Math. Meth. Appl. Sci. 3 (1981), 475-487.
    • (1981) Math. Meth. Appl. Sci. , vol.3 , pp. 475-487
    • Colton, D.1    Kress, R.2
  • 16
    • 1542534864 scopus 로고
    • Singular perturbations I. Spaces and singular perturbations in manifolds without boundary
    • North-Holland
    • L.S. Frank, Singular perturbations I. Spaces and singular perturbations in manifolds without boundary. Studies in Mathematics and its Applications. North-Holland (1990).
    • (1990) Studies in Mathematics and Its Applications
    • Frank, L.S.1
  • 17
    • 0022056511 scopus 로고
    • The integral equation method in electromagnetic scattering
    • G.A. Gray and R.E. Kleinman. The integral equation method in electromagnetic scattering. J. Math. Anal. Appl., 107 (1985), 455-477.
    • (1985) J. Math. Anal. Appl. , vol.107 , pp. 455-477
    • Gray, G.A.1    Kleinman, R.E.2
  • 21
    • 0016535535 scopus 로고
    • An impedance sheet approximation for thin dielectric shells
    • R.F. Harrington and J.R. Mautz, An impedance sheet approximation for thin dielectric shells, IEEE Trans. Antennas Propagt, 23 (1975), 531-534.
    • (1975) IEEE Trans. Antennas Propagt , vol.23 , pp. 531-534
    • Harrington, R.F.1    Mautz, J.R.2
  • 22
    • 0028497265 scopus 로고
    • Higher order impedance boundary conditions revisited : Application to chiral coatings
    • D.J. Hoppe and Y. Rahmat-Samii, Higher order impedance boundary conditions revisited : application to chiral coatings, J. Elect. Waves and Appl., 8 (1994), 1303-1329.
    • (1994) J. Elect. Waves and Appl. , vol.8 , pp. 1303-1329
    • Hoppe, D.J.1    Rahmat-Samii, Y.2
  • 23
    • 84980151986 scopus 로고
    • Radiation boundary conditions for acoustic and elastic wave calculations
    • B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations. Commun. Pure Appl. Math., 32 (1977), 629-651.
    • (1977) Commun. Pure Appl. Math. , vol.32 , pp. 629-651
    • Engquist, B.1    Majda, A.2
  • 25
    • 0002951131 scopus 로고
    • Universal boundary conditions of the electromagnetic field
    • M. Idemen, Universal boundary conditions of the electromagnetic field. J Phys. Soc. Japan, 59(1990), 71-80.
    • (1990) J Phys. Soc. Japan , vol.59 , pp. 71-80
    • Idemen, M.1
  • 26
    • 0003133730 scopus 로고
    • Generalized impedance boundary conditions for surface wave structures
    • ed. J. Drown Pergamon Press. New York
    • S.N. Karp and F.C. Karal. Generalized impedance boundary conditions for surface wave structures. Electromagnetic Wave Theory. Part I. ed. J. Drown (1965), 479-483, Pergamon Press. New York.
    • (1965) Electromagnetic Wave Theory , Issue.PART I , pp. 479-483
    • Karp, S.N.1    Karal, F.C.2
  • 28
    • 0021936870 scopus 로고
    • The Robin problem for the Helmholtz equation as a singular perturbation problem
    • A. Kirsch, The Robin problem for the Helmholtz equation as a singular perturbation problem, Numer. Funct. Anal. Optimiz, 8 (1) (1985), 1-20.
    • (1985) Numer. Funct. Anal. Optimiz , vol.8 , Issue.1 , pp. 1-20
    • Kirsch, A.1
  • 29
    • 0018542262 scopus 로고
    • On the exterior boundary-value problem for the time-harmonic Maxwell equations
    • W. Knauff and R. Kress. On the exterior boundary-value problem for the time-harmonic Maxwell equations, J. Math. Anal. Appl., 72 (1979), 215-235.
    • (1979) J. Math. Anal. Appl. , vol.72 , pp. 215-235
    • Knauff, W.1    Kress, R.2
  • 30
    • 0003057304 scopus 로고
    • On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies
    • R. Kress. On the limiting behaviour of solutions to boundary integral equations associated with time harmonic wave equations for small frequencies, Math. Meth. Appl. Sci. 1 (1979), 89-100.
    • (1979) Math. Meth. Appl. Sci. , vol.1 , pp. 89-100
    • Kress, R.1
  • 31
    • 84983965081 scopus 로고
    • On the existence of a solution to a singular integral equation in electromagnetic reflection
    • R. Kress. On the existence of a solution to a singular integral equation in electromagnetic reflection. J. Math. Anal. Appl., 77 (1980), 555-566.
    • (1980) J. Math. Anal. Appl. , vol.77 , pp. 555-566
    • Kress, R.1
  • 32
    • 0001029596 scopus 로고
    • div (Γ) et nature de l'opérateur de Steklov-Poincaré du problème extérieur de l'électromagnétisme
    • div (Γ) et nature de l'opérateur de Steklov-Poincaré du problème extérieur de l'électromagnétisme. C. R. Acad. Sci. Paris. Série I. 316 (1993), 369-372.
    • (1993) C. R. Acad. Sci. Paris. Série I , vol.316 , pp. 369-372
    • De La Bourdonnaye, A.1
  • 34
    • 34250923661 scopus 로고
    • Zur formulierung eines allgemeiner beugung problems durch eine integralgleichung
    • A.W. Maue, Zur formulierung eines allgemeiner beugung problems durch eine integralgleichung. Z. Phys., 126 (1949), 601-618.
    • (1949) Z. Phys. , vol.126 , pp. 601-618
    • Maue, A.W.1
  • 35
    • 0009304641 scopus 로고
    • Über die beugung elektromagnetischer schwingungen an endlichen homogenen körpern
    • C. Müller. Über die beugung elektromagnetischer schwingungen an endlichen homogenen körpern. Math. Ann., 123 (1951), 345-378.
    • (1951) Math. Ann. , vol.123 , pp. 345-378
    • Müller, C.1
  • 37
    • 0000527853 scopus 로고
    • Approximation par potentiel de double couche du problème de Neumann extérieur
    • J.C. Nédélec. Approximation par potentiel de double couche du problème de Neumann extérieur. C. R. Acad. Sci. Paris. 280 (1978), 103-106.
    • (1978) C. R. Acad. Sci. Paris. , vol.280 , pp. 103-106
    • Nédélec, J.C.1
  • 39
    • 0019634910 scopus 로고
    • Exterior boundary value problems as limits of interface problems
    • A.G. Ramm. Exterior boundary value problems as limits of interface problems, J. Math. Anal. Appl., 84 (1981), 256-263.
    • (1981) J. Math. Anal. Appl. , vol.84 , pp. 256-263
    • Ramm, A.G.1
  • 40
    • 0009155597 scopus 로고
    • Skin-effect by a perturbation method
    • S.M. Rytov. Skin-effect by a perturbation method, J. Phys. USSR. 2 (1940), 233-242.
    • (1940) J. Phys. USSR , vol.2 , pp. 233-242
    • Rytov, S.M.1
  • 41
    • 0009155598 scopus 로고
    • On solutions of Maxwell's equations in an exterior region
    • U. Saunders. On solutions of Maxwell's equations in an exterior region. Proc. Nat. Acad. Sci. U.S.A., 38 (1952), 342-348.
    • (1952) Proc. Nat. Acad. Sci. U.S.A. , vol.38 , pp. 342-348
    • Saunders, U.1
  • 43
    • 0009235543 scopus 로고
    • Approximate boundary conditions for homogeneous dielectric bodies
    • T.B.A. Senior. Approximate boundary conditions for homogeneous dielectric bodies, J. Elect. Waves Appl., 9(1995) 1227-1239.
    • (1995) J. Elect. Waves Appl. , vol.9 , pp. 1227-1239
    • Senior, T.B.A.1
  • 44
    • 0024915734 scopus 로고
    • Derivation and application of a class of generalized boundary conditions
    • T.B.A. Senior and J.L. Yolakis. Derivation and application of a class of generalized boundary conditions. IEEE Trans. Antennas Propagt. 37 (1989).
    • (1989) IEEE Trans. Antennas Propagt. , vol.37
    • Senior, T.B.A.1    Yolakis, J.L.2
  • 45
    • 0026240378 scopus 로고
    • Generalized impedance boundary conditions in scattering
    • T.B.A. Senior and J.L. Volakis. Generalized impedance boundary conditions in scattering. Proc. IEEE. 79 (1991), 1413-1420.
    • (1991) Proc. IEEE , vol.79 , pp. 1413-1420
    • Senior, T.B.A.1    Volakis, J.L.2
  • 46
    • 0028750399 scopus 로고
    • Scattering by a circular impedance cylinder coated with a composite anisotropic chiral sheath
    • Z.X. Shen. Scattering by a circular impedance cylinder coated with a composite anisotropic chiral sheath, J. Elect. Waves and Appl., 8 (1994). 1625-1644.
    • (1994) J. Elect. Waves and Appl. , vol.8 , pp. 1625-1644
    • Shen, Z.X.1
  • 48
    • 0009301639 scopus 로고
    • On an integral equation in elctromagnetic diffraction theory
    • P. Werner, On an integral equation in elctromagnetic diffraction theory. J. Math. Anal. Appl., 14 (1966), 445-462.
    • (1966) J. Math. Anal. Appl. , vol.14 , pp. 445-462
    • Werner, P.1
  • 49
    • 0009227612 scopus 로고
    • Ein grenzübergang in der theorie akustischer wellenfelder
    • P. Werner, Ein grenzübergang in der theorie akustischer wellenfelder, Arch. Rat. Mech. Anal. 33 (1969), 192-218.
    • (1969) Arch. Rat. Mech. Anal. , vol.33 , pp. 192-218
    • Werner, P.1
  • 50
    • 0000727886 scopus 로고
    • Die natürlichen randwertaufgaben im aussenraum für strahlnngsfelder beliebigen dimension und beliebiger rnges
    • H. Weyl, Die natürlichen randwertaufgaben im aussenraum für strahlnngsfelder beliebigen dimension und beliebiger rnges, Math. Z., 56 (1952), 105.
    • (1952) Math. Z. , vol.56 , pp. 105
    • Weyl, H.1
  • 51
    • 0023401557 scopus 로고
    • The limiting behaviour of solutions of the acoustic transmission problems
    • P. Wilde. The limiting behaviour of solutions of the acoustic transmission problems. J. Math. Anal. Appl., 126 (1987), 24-38.
    • (1987) J. Math. Anal. Appl. , vol.126 , pp. 24-38
    • Wilde, P.1


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