The stability of numerical approximations of the time domain current induced on thin wire and strip antennas

Applied Numerical Mathematics

Volumn 55, Issue 1, 2005, Pages 48-68

  Davies, Penny J ^a   Duncan, Dugald B ^b   Zubik Kowal, Barbara ^c  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b HERIOT WATT UNIVERSITY   (United Kingdom)

^c BOISE STATE UNIVERSITY   (United States)

Author keywords

Retarded potential; Stability; Thin strip; Thin wire; Time domain

Indexed keywords

ANTENNAS; APPROXIMATION THEORY; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; ELECTRIC CURRENTS; ELECTRIC FIELD EFFECTS; ELECTRIC WIRE; ELECTROMAGNETIC PULSE; LINEAR EQUATIONS; PROBLEM SOLVING; STABILITY;

RETARDED POTENTIAL; THIN STRIP; THIN WIRE; TIME DOMAIN;

TIME DOMAIN ANALYSIS;

EID: 21844431632     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apnum.2004.10.007     Document Type: Article

References (21)

1. P.J. Davies Numerical stability and convergence of approximations of retarded potential integral equations SIAM J. Numer. Anal. 31 1994 856 875
2. P.J. Davies On the numerical stability of schemes for time domain scattering from a thin strip G.C. Cohen E. Heikkola P. Joly P. Neittaanmäki Mathematical and Numerical Aspects of Wave Propagation 2003 Springer Berlin 776 781
3. P.J. Davies, and D.B. Duncan Time-marching numerical schemes for the electric field integral equation on a straight thin wire Adv. Comp. Math. 2 1994 279 317
4. P.J. Davies, and D.B. Duncan Averaging techniques for time marching schemes for retarded potential integral equations Appl. Numer. Math. 23 1997 291 310
5. P.J. Davies, and D.B. Duncan Stability and convergence of collocation schemes for retarded potential integral equations SIAM J. Numer. Anal. 42 3 2004 1167 1188
6. P.J. Davies, B.P. Rynne, and B. Zubik-Kowal The time domain integral equation for a straight thin wire antenna with the reduced kernel is not well-posed IEEE Trans. Ant. Prop. 50 8 2002 1165 1166
7. C.J. Gladwin, and R. Jeltsch Stability of quadrature rule methods for first kind Volterra integral equations BIT 14 1974 144 151
8. I.S. Gradshteyn, and I.M. Ryzhik Table of Integrals, Series, and Products fifth ed. 1994 Academic Press New York
9. T. Ha-Duong On retarded potential boundary integral equations and their discretisation M. Ainsworth P.J. Davies D.B. Duncan P.A. Martin B.P. Rynne Topics in Computational Wave Propagation: Direct and Inverse Problems 2003 Springer Berlin 301 336
10. D.S. Jones Theory of Electromagnetism 1964 Oxford Univ. Press Oxford
11. D.S. Jones Note on the integral equation for a straight wire antenna IEE Proc. 128 1981 114 116
12. D.S. Jones Methods in Electromagnetic Wave Propagation second ed. 1994 Clarendon Press Oxford
13. J.G. Jones On the numerical solution of convolution integral equations and systems of such equations Math. Comp. 15 1961 131 142
14. P. Linz Analytical and Numerical Methods for Volterra Equations 1985 SIAM Philadelphia, PA
15. E.K. Miller, and J.A. Landt Direct time-domain techniques for transient radiation and scattering from wires Proc. IEEE 68 1980 1396 1423
16. B.P. Rynne The well-posedness of the integral equations for thin wire antennas IMA J. Appl. Math. 49 1992 35 44
17. B.P. Rynne, and P.D. Smith Stability of time marching algorithms for the electric field equation J. Electromag. Waves Appl. 4 1990 1181 1205
18. S.A. Schelkunoff Advanced Antenna Theory 1952 Wiley New York
19. A.G. Tijhuis, P. Zhongqui, and A.R. Bretones Transient excitation of a straight thin wire segment: a new look at an old problem IEEE Trans. Antennas Propagation 40 1992 1132 1146
20. B. Zubik-Kowal, and P.J. Davies Numerical approximation of time domain electromagnetic scattering from a thin wire Numer. Algorithms 30 2002 25 36
21. B. Zubik-Kowal, and P.J. Davies Fourier stability analysis of a numerical method for time domain electromagnetic scattering from a thin wire Numer. Algorithms 35 2004 121 130