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Volumn 42, Issue 3, 2004, Pages 1167-1188

Stability and convergence of collocation schemes for retarded potential integral equations

Author keywords

Boundary integral; Convergence; Retarded potential; Stability

Indexed keywords

ACOUSTIC WAVE SCATTERING; COMPUTATIONAL METHODS; CONVERGENCE OF NUMERICAL METHODS; ELECTROMAGNETIC WAVE SCATTERING; FINITE ELEMENT METHOD; FOURIER TRANSFORMS; LAPLACE TRANSFORMS; STABILITY; TIME DOMAIN ANALYSIS;

EID: 21244452426     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142901395321     Document Type: Article
Times cited : (102)

References (33)
  • 2
    • 0346577046 scopus 로고
    • Time dependent integral equations for the Maxwell system
    • A. BACHELOT AND A. PUJOLS, Time dependent integral equations for the Maxwell system, C. R. Acad. Sci. Paris Sér. I Math., 314 (1992), pp. 639-644.
    • (1992) C. R. Acad. Sci. Paris Sér. I Math. , vol.314 , pp. 639-644
    • Bachelot, A.1    Pujols, A.2
  • 3
    • 84988202061 scopus 로고
    • Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (i)
    • A. BAMBERGER AND T. HA-DUONG, Formulation variationnelle espace-temps pour le calcul par potentiel retardé de la diffraction d'une onde acoustique (i). Math. Methods Appl. Sci., 8 (1986), pp. 405-435.
    • (1986) Math. Methods Appl. Sci. , vol.8 , pp. 405-435
    • Bamberger, A.1    Ha-Duong, T.2
  • 4
    • 0014749272 scopus 로고
    • Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation
    • J. H. BRAMBLE AND S. R. HILBERT, Estimation of linear functionals on Sobolev spaces with applications to Fourier transforms and spline interpolation, SIAM J. Numer. Anal., 7 (1970), pp. 112-124.
    • (1970) SIAM J. Numer. Anal. , vol.7 , pp. 112-124
    • Bramble, J.H.1    Hilbert, S.R.2
  • 5
    • 0003081462 scopus 로고    scopus 로고
    • A fast, high-order algorithm for the solution of surf ace scattering problems: Basic implementation, tests and applications
    • O. BRUNO AND L. KUNYANSKY, A fast, high-order algorithm for the solution of surf ace scattering problems: basic implementation, tests and applications, J. Comput. Phys., 169 (2001), pp. 80-110.
    • (2001) J. Comput. Phys. , vol.169 , pp. 80-110
    • Bruno, O.1    Kunyansky, L.2
  • 6
    • 0028444761 scopus 로고
    • Numerical stability and convergence of approximations of retarded potential integral equations
    • P. J. DAVIES, Numerical stability and convergence of approximations of retarded potential integral equations, SIAM J. Numer. Anal., 31 (1994), pp. 856-875.
    • (1994) SIAM J. Numer. Anal. , vol.31 , pp. 856-875
    • Davies, P.J.1
  • 7
    • 0027927289 scopus 로고
    • Stability of time-marching numerical schemes for the electric field integral equation
    • P. J. DAVIES, Stability of time-marching numerical schemes for the electric field integral equation, J. Electromag. Waves Appl., 8 (1994), pp. 85-114.
    • (1994) J. Electromag. Waves Appl. , vol.8 , pp. 85-114
    • Davies, P.J.1
  • 8
    • 0032068884 scopus 로고    scopus 로고
    • A stability analysis of a time marching scheme for the general surface electric field integral equation
    • P. J. DAVIES, A stability analysis of a time marching scheme for the general surface electric field integral equation, Appl. Numer. Math., 27 (1998), pp. 33-57.
    • (1998) Appl. Numer. Math. , vol.27 , pp. 33-57
    • Davies, P.J.1
  • 9
    • 21244499376 scopus 로고
    • Accuracy and convergence of time marching schemes for RPIEs
    • University of Dundee, Dundee, Scotland
    • P. J. DAVIES AND D. B. DUNCAN, Accuracy and Convergence of Time Marching Schemes for RPIEs, Technical report, University of Dundee, Dundee, Scotland, 1995.
    • (1995) Technical Report
    • Davies, P.J.1    Duncan, D.B.2
  • 10
    • 0031146877 scopus 로고    scopus 로고
    • Averaging techniques for time-marching schemes for retarded potential integral equations
    • P. J. DAVIES AND D. B. DUNCAN, Averaging techniques for time-marching schemes for retarded potential integral equations, Appl. Numer. Math., 23 (1997), pp. 291-310.
    • (1997) Appl. Numer. Math. , vol.23 , pp. 291-310
    • Davies, P.J.1    Duncan, D.B.2
  • 11
    • 21244476786 scopus 로고    scopus 로고
    • Numerical stability of collocation schemes for time domain boundary integral equations
    • Kiel, 2001, C. Carstensen, S. A. Funken, W. Hackbusch, R. H. W. Hoppe, and P. Monk, eds., Springer-Verlag, New York
    • P. J. DAVIES AND D. B. DUNCAN, Numerical stability of collocation schemes for time domain boundary integral equations, in Computational Electromagnetics: Proceedings of the GAMM Workshop, Kiel, 2001, C. Carstensen, S. A. Funken, W. Hackbusch, R. H. W. Hoppe, and P. Monk, eds., Springer-Verlag, New York, 2003, pp. 51-67.
    • (2003) Computational Electromagnetics: Proceedings of the GAMM Workshop , pp. 51-67
    • Davies, P.J.1    Duncan, D.B.2
  • 13
    • 0021500970 scopus 로고
    • The study of a petrov-galerkin method for first-order hyperbolic equations
    • D. B. DUNCAN AND D. F. GRIFFITHS, The study of a Petrov-Galerkin method for first-order hyperbolic equations, Comput. Methods Appl. Mech. Engrg., 45 (1984), pp. 147-166.
    • (1984) Comput. Methods Appl. Mech. Engrg. , vol.45 , pp. 147-166
    • Duncan, D.B.1    Griffiths, D.F.2
  • 14
    • 0026402823 scopus 로고
    • Jacobi iteration in implicit difference schemes for the wave equation
    • D. B. DUNCAN AND M. A. M. LYNCH, Jacobi iteration in implicit difference schemes for the wave equation, SIAM J. Numer. Anal., 28 (1991), pp. 1661-1679.
    • (1991) SIAM J. Numer. Anal. , vol.28 , pp. 1661-1679
    • Duncan, D.B.1    Lynch, M.A.M.2
  • 15
    • 0032595029 scopus 로고    scopus 로고
    • The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena
    • A. A. ERGIN, B. SHANKER, AND E. MICHIELSSEN, The plane-wave time-domain algorithm for the fast analysis of transient wave phenomena, IEEE Ant. Prop. Magazine, 41 (1999), pp. 39-52.
    • (1999) IEEE Ant. Prop. Magazine , vol.41 , pp. 39-52
    • Ergin, A.A.1    Shanker, B.2    Michielssen, E.3
  • 16
    • 0034088879 scopus 로고    scopus 로고
    • Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm
    • A. A. ERGIN, B. SHANKER, AND E. MICHIELSSEN, Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm, J. Acoust. Soc. Am., 107 (2000), pp. 1168-1178.
    • (2000) J. Acoust. Soc. Am. , vol.107 , pp. 1168-1178
    • Ergin, A.A.1    Shanker, B.2    Michielssen, E.3
  • 17
    • 21244463143 scopus 로고
    • Stability of quadrature rule methods for first kind Volterra integral equations
    • C. J. GLADWIN AND R. JELTSCH, Stability of quadrature rule methods for first kind Volterra integral equations, BIT, 14 (1974), pp. 144-151.
    • (1974) BIT , vol.14 , pp. 144-151
    • Gladwin, C.J.1    Jeltsch, R.2
  • 19
    • 0040162209 scopus 로고
    • On the transient acoustic scattering by a flat object
    • T. HA-DUONG, On the transient acoustic scattering by a flat object, Japan J. Appl. Math., 7 (1990), pp. 489-513.
    • (1990) Japan J. Appl. Math. , vol.7 , pp. 489-513
    • Ha-Duong, T.1
  • 20
    • 21244496404 scopus 로고    scopus 로고
    • On retarded potential boundary integral equations and their discretisation
    • M. Ainsworth, P. J. Davies, D. B. Duncan, P. A. Martin, and B. P. Rynne, eds., Springer-Verlag, New York
    • T. HA-DUONG, On retarded potential boundary integral equations and their discretisation, in Topics in Computational Wave Propagation: Direct and Inverse Problems, M. Ainsworth, P. J. Davies, D. B. Duncan, P. A. Martin, and B. P. Rynne, eds., Springer-Verlag, New York, 2003, pp. 301-336.
    • (2003) Topics in Computational Wave Propagation: Direct and Inverse Problems , pp. 301-336
    • Ha-Duong, T.1
  • 23
    • 84968478888 scopus 로고
    • On the numerical solution of convolution integral equations and systems of such equations
    • J. G. JONES, On the numerical solution of convolution integral equations and systems of such equations, Math. Comp., 15 (1961), pp. 131-142.
    • (1961) Math. Comp. , vol.15 , pp. 131-142
    • Jones, J.G.1
  • 26
    • 0001367098 scopus 로고    scopus 로고
    • Fast evaluation of two-dimensional transient wave fields
    • M. LU, J. WANG, A. A. ERGIN, AND E. MICHIELSSEN, Fast evaluation of two-dimensional transient wave fields, J. Comput. Phys., 158 (2000), pp. 161-185.
    • (2000) J. Comput. Phys. , vol.158 , pp. 161-185
    • Lu, M.1    Wang, J.2    Ergin, A.A.3    Michielssen, E.4
  • 27
    • 84951609873 scopus 로고
    • On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations
    • C. LUBICH, On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations, Numer., Math., 67 (1994), pp. 365-389.
    • (1994) Numer., Math. , vol.67 , pp. 365-389
    • Lubich, C.1
  • 29
    • 84947143087 scopus 로고
    • Time domain scattering from arbitrary surfaces using the electric field equation
    • B. P. RYNNE, Time domain scattering from arbitrary surfaces using the electric field equation, J. Electromagn. Waves Appl., 5 (1991), pp. 93-112.
    • (1991) J. Electromagn. Waves Appl. , vol.5 , pp. 93-112
    • Rynne, B.P.1
  • 30
    • 0010785631 scopus 로고    scopus 로고
    • The well-posedness of the electric field integral equation for transient scattering from a perfectly conducting body
    • B. P. RYNNE, The well-posedness of the electric field integral equation for transient scattering from a perfectly conducting body, Math. Methods Appl. Sci., 22 (1999), pp. 619-631.
    • (1999) Math. Methods Appl. Sci. , vol.22 , pp. 619-631
    • Rynne, B.P.1
  • 31
    • 0001262342 scopus 로고
    • Stability of time marching algorithms for the electric field equation
    • B. P. RYNNE AND P. D. SMITH, Stability of time marching algorithms for the electric field equation, J. Electromagn. Waves Appl., 4 (1990), pp. 1181-1205.
    • (1990) J. Electromagn. Waves Appl. , vol.4 , pp. 1181-1205
    • Rynne, B.P.1    Smith, P.D.2
  • 32
    • 21244442295 scopus 로고
    • The real zeros of Struve's function
    • J. STEINIG, The real zeros of Struve's function, SIAM J. Math. Anal., 1 (1970), pp. 365-375.
    • (1970) SIAM J. Math. Anal. , vol.1 , pp. 365-375
    • Steinig, J.1
  • 33
    • 0005654340 scopus 로고
    • Numerische, inbesondere approximationstheoretische Behandlung von Funktionalgleichungen
    • A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin
    • V. THOMÉE, Convergence estimates for semi-discrete Galerkin methods for initial-value problems, in Numerische, inbesondere approximationstheoretische Behandlung von Funktionalgleichungen, Lecture Notes in Math. 333, A. Dold and B. Eckmann, eds., Springer-Verlag, Berlin, 1973, pp. 243-262.
    • (1973) Lecture Notes in Math. , vol.333 , pp. 243-262
    • Thomée, V.1


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