iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/BF02521113
Time-marching numerical schemes for the electric field integral equation on a straight thin wire | Advances in Computational Mathematics Skip to main content
Springer Nature Link
Log in

Time-marching numerical schemes for the electric field integral equation on a straight thin wire

  • Published:
Advances in Computational Mathematics Aims and scope Submit manuscript

Abstract

We derive and analyse four algorithms for computing the current induced on a thin straight wire by a transient electric field. They all involve solving the thin wire electric field integral equations (EFIEs) and consist of a very accurate differential equations solver together with various schemes to approximate the vector potential integral equation. We carry out a rigorous numerical stability analysis of each of these methods. This has not previously been done for solution schemes for the thin wire EFIEs. Each scheme is shown to be stable and convergent provided the radius of the wire is small enough for the thin wire equations to be a valid model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A.R. Bretones, R.G. Martin and A. Salinas, Dotig1, a time-domain numerical code for the study of the interaction of electromagnetic pulses with thin-wire structures, COMPEL 8(1989)39–61.

    Google Scholar 

  2. R. Courant and D. HilbertMethods of Mathematical Physics, Vol. 2:Partial Differential Equations (Wiley, 1962).

  3. P.J. Davies, Numerical stability and convergence of approximations of retarded potential integral equations, SIAM J. Numer. Anal., to appear.

  4. P.J. Davies, Stability of time-marching numerical schemes for the electric field integral equation, J. Electromag. Waves Appl. 8(1994)85–114.

    Google Scholar 

  5. D. S. Jones,Theory of Electromagnetism (Oxford University Press, 1964).

  6. D.S. Jones,Acoustic and Electromagnetic Waves (Oxford University Press, 1986).

  7. R.G. Martin, A. Salinas and A.R. Bretones, Time-domain integral equation methods for transient analysis, IEEE A&P 34(1992)15–22.

    Google Scholar 

  8. J.H. Mathews,Numerical Methods for Mathematics, Science and Engineering, 2nd ed. (Prentice-Hall, 1992).

  9. E.K. Miller, A.J. Poggio and G.J. Burke, An integro-differential equation technique for the time-domain analysis of thin wire structures. I. The numerical method, J. Comp. Phys. 12(1973)24–48.

    Article  MATH  Google Scholar 

  10. E.K. Miller, A.J. Poggio and G.J. Burke, An integro-differential equation technique for the timedomain analysis of thin wire structures. II. Numerical results, J. Comp. Phys. 12(1973)210–233.

    Article  MATH  Google Scholar 

  11. E.K. Miller and J.A. Landt, Direct time-domain techniques for transient radiation and scattering from wires, Proc. IEEE 68(1980)1396–1423.

    Article  Google Scholar 

  12. A.R. Mitchell and D.F. Griffiths,The Finite Difference Method in Partial Differential Equations (Wiley, 1980).

  13. R.D. Richtmyer and K.W. Morton,Difference Methods for Initial Value Problems (Interscience, 1967).

  14. B.P. Rynne, Stability and convergence of time marching methods in scattering problems, IMA J. Appl. Math. 35(1985)297–310.

    MATH  MathSciNet  Google Scholar 

  15. B.P. Rynne and P.D. Smith, Stability of time marching algorithms for the electric field equations, J. Electromag. Waves Appl. 4(1990)1181–1205.

    Article  Google Scholar 

  16. A. Salinas, A.R. Bretones, R.G. Martin and J. Fornieles, An improvement of the dotig1 code,IEE Int. Conf. on Comp. Electromag. (1991) pp. 222–225.

  17. A.G. Tijhuis, Toward a stable marching on in time method for two dimensional transient electromagnetic scattering problems, Radio Science 19(1984)1311–1317.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, The University, DD1 4HN, Dundee, UK

    Penny J. Davies

  2. Department of Mathematics, Heriot-Watt University, Riccarton, EH14 4AS, Edinburgh, UK

    Dugald B. Duncan

Authors
  1. Penny J. Davies
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dugald B. Duncan
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Davies, P.J., Duncan, D.B. Time-marching numerical schemes for the electric field integral equation on a straight thin wire. Adv Comput Math 2, 279–317 (1994). https://doi.org/10.1007/BF02521113

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02521113

Keywords

AMS(MOS) subject classification

Search

Navigation