Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A stabilized time-domain combined field integral equation using the quasi-Helmholtz projectors (2312.06367v2)

Published 11 Dec 2023 in math.NA and cs.NA

Abstract: This paper introduces a time-domain combined field integral equation for electromagnetic scattering by a perfect electric conductor. The new equation is obtained by leveraging the quasi-Helmholtz projectors, which separate both the unknown and the source fields into solenoidal and irrotational components. These two components are then appropriately rescaled to cure the solution from a loss of accuracy occurring when the time step is large. Yukawa-type integral operators of a purely imaginary wave number are also used as a Calderon preconditioner to eliminate the ill-conditioning of matrix systems. The stabilized time-domain electric and magnetic field integral equations are linearly combined in a Calderon-like fashion, then temporally discretized using an appropriate pair of trial functions, resulting in a marching-on-in-time linear system. The novel formulation is immune to spurious resonances, dense discretization breakdown, large-time step breakdown and dc instabilities stemming from non-trivial kernels. Numerical results for both simply-connected and multiply-connected scatterers corroborate the theoretical analysis.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (35)
  1. K. Cools, F. P. Andriulli, F. Olyslager, and E. Michielssen, “Time domain Calderón identities and their application to the integral equation analysis of scattering by PEC objects Part I: Preconditioning,” IEEE Trans. Antennas Propag., vol. 57, no. 8, pp. 2352–2364, 2009.
  2. F. P. Andriulli, K. Cools, F. Olyslager, and E. Michielssen, “Time domain Calderón identities and their application to the integral equation analysis of scattering by PEC objects Part II: Stability,” IEEE Trans. Antennas Propag., vol. 57, no. 8, pp. 2365–2375, 2009.
  3. Y. Shi, H. Bagci, and M. Lu, “On the static loop modes in the marching-on-in-time solution of the time-domain electric field integral equation,” IEEE Antennas Wirel. Propag. Lett., vol. 13, pp. 317–320, 2014.
  4. A. F. Peterson, “Observed baseline convergence rates and superconvergence in the scattering cross section obtained from numerical solutions of the MFIE,” IEEE Trans. Antennas Propag., vol. 56, no. 11, pp. 3510–3515, 2008.
  5. L. Gurel and O. Ergul, “Contamination of the accuracy of the combined-field integral equation with the discretization error of the magnetic-field integral equation,” IEEE Trans. Antennas Propag., vol. 57, no. 9, pp. 2650–2657, 2009.
  6. K. Cools, F. P. Andriulli, F. Olyslager, and E. Michielssen, “Nullspaces of MFIE and Calderón preconditioned EFIE operators applied to toroidal surfaces,” IEEE Trans. Antennas Propag., vol. 57, no. 10, pp. 3205–3215, 2009.
  7. J.-S. Zhao and W. C. Chew, “Integral equation solution of Maxwell’s equations from zero frequency to microwave frequencies,” IEEE Trans. Antennas Propag., vol. 48, no. 10, pp. 1635–1645, 2000.
  8. Y. Zhang, T. J. Cui, W. C. Chew, and J.-S. Zhao, “Magnetic field integral equation at very low frequencies,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1864–1871, 2003.
  9. Z.-G. Qian and W. C. Chew, “Enhanced A-EFIE with perturbation method,” IEEE Trans. Antennas Propag., vol. 58, no. 10, pp. 3256–3264, 2010.
  10. I. Bogaert, K. Cools, F. P. Andriulli, and H. Bagci, “Low-frequency scaling of the standard and mixed magnetic field and Müller integral equations,” IEEE Trans. Antennas Propag., vol. 62, no. 2, pp. 822–831, 2014.
  11. D. S. Weile, G. Pisharody, N.-W. Chen, B. Shanker, and E. Michielssen, “A novel scheme for the solution of the time-domain integral equations of electromagnetics,” IEEE Trans. Antennas Propag., vol. 52, no. 1, pp. 283–295, 2004.
  12. G. Pisharody and D. S. Weile, “Robust solution of time-domain integral equations using loop-tree decomposition and bandlimited extrapolation,” IEEE Trans. Antennas Propag., vol. 53, no. 6, pp. 2089–2098, 2005.
  13. H. A. Ülkü, I. Bogaert, K. Cools, F. P. Andriulli, and H. Bağci, “Mixed discretization of the time-domain MFIE at low frequencies,” IEEE Antennas Wirel. Propag. Lett., vol. 16, pp. 1565–1568, 2017.
  14. B. Shanker, A. A. Ergin, K. Aygun, and M. Michielssen, “Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral equation,” IEEE Trans. Antennas Propag., vol. 48, no. 7, pp. 1064–1074, 2000.
  15. Y. Beghein, K. Cools, H. Bagci, and D. De Zutter, “A space-time mixed Galerkin marching-on-in-time scheme for the time-domain combined field integral equation,” IEEE Trans. Antennas Propag., vol. 61, no. 3, pp. 1228–1238, 2013.
  16. A. E. Yilmaz, J.-M. Jin, and E. Michielssen, “Analysis of low-frequency electromagnetic transients by an extended time-domain adaptive integral method,” IEEE Trans. Compon. Packag., vol. 30, no. 2, pp. 301–312, 2007.
  17. X. Tian, G. Xiao, and J. Fang, “Application of loop-flower basis functions in the time-domain electric field integral equation,” IEEE Transactions on Antennas and Propagation, vol. 63, no. 3, pp. 1178–1181, 2015.
  18. F. P. Andriulli, K. Cools, I. Bogaert, and E. Michielssen, “On a well-conditioned electric field integral operator for multiply connected geometries,” IEEE Trans. Antennas Propag., vol. 61, no. 4, pp. 2077–2087, 2013.
  19. Y. Beghein, K. Cools, and F. P. Andriulli, “A DC stable and large-time step well-balanced TD-EFIE based on quasi-Helmholtz projectors,” IEEE Trans. Antennas Propag., vol. 63, no. 7, pp. 3087–3097, 2015.
  20. ——, “A DC-stable, well-balanced, Calderón preconditioned time domain electric field integral equation,” IEEE Trans. Antennas Propag., vol. 63, no. 12, pp. 5650–5660, 2015.
  21. A. Merlini, Y. Beghein, K. Cools, E. Michielssen, and F. P. Andriulli, “Magnetic and combined field integral equations based on the quasi-Helmholtz projectors,” IEEE Trans. Antennas Propag., vol. 68, no. 5, pp. 3834–3846, 2020.
  22. O. Steinbach and M. Windisch, “Modified combined field integral equations for electromagnetic scattering,” SIAM J. Numer. Anal., vol. 47, no. 2, pp. 1149–1167, 2009.
  23. V. C. Le, P. Cordel, F. P. Andriulli, and K. Cools, “A Yukawa-Calderón time-domain combined field integral equation for electromagnetic scattering,” in Proc. Int. Conf. Electromagn. Adv. Appl. (ICEAA), 2023.
  24. S. Rao, D. Wilton, and A. Glisson, “Electromagnetic scattering by surfaces of arbitrary shape,” IEEE Trans. Antennas Propag., vol. AP-30, no. 3, pp. 409–418, 1982.
  25. A. Buffa and S. H. Christiansen, “A dual finite element complex on the barycentric refinement,” Math. Comput., vol. 76, no. 260, pp. 1743–1770, 2007.
  26. K. Cools, F. P. Andriulli, D. De Zutter, and E. Michielssen, “Accurate and conforming mixed discretization of the MFIE,” IEEE Antennas Wirel. Propag. Lett., vol. 10, pp. 528–531, 2011.
  27. G. Vecchi, “Loop-star decomposition of basis functions in the discretization of the EFIE,” IEEE Trans. Antennas Propag., vol. 47, no. 2, pp. 339–346, 1999.
  28. J.-F. Lee, R. Lee, and R. J. Burkholder, “Loop star basis functions and a robust preconditioner for EFIE scattering problems,” IEEE Trans. Antennas Propag., vol. 51, no. 8, pp. 1855–1863, 2003.
  29. F. P. Andriulli, “Loop-star and loop-tree decompositions: Analysis and efficient algorithms,” IEEE Trans. Antennas Propag., vol. 60, no. 5, pp. 2347–2356, 2012.
  30. M. B. Stephanson and J.-F. Lee, “Preconditioned electric field integral equation using Calderon identities and dual loop/star basis functions,” IEEE Trans. Antennas Propag., vol. 57, no. 4, pp. 1274–1279, 2009.
  31. S. Yan, J.-M. Jin, and Z. Nie, “EFIE analysis of low-frequency problems with loop-star decomposition and Calderón multiplicative preconditioner,” IEEE Trans. Antennas Propag., vol. 58, no. 3, pp. 857–867, 2010.
  32. F. P. Andriulli, K. Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, “A multiplicative Calderon preconditioner for the electric field integral equation,” IEEE Trans. Antennas Propag., vol. 56, no. 8, pp. 2398–2412, 2008.
  33. V. C. Le and K. Cools, “A well-conditioned combined field integral equation for electromagnetic scattering,” submitted for publication, 2023.
  34. R. Kress, “Minimizing the condition number of boundary integral operators in acoustic and electromagnetic scattering,” Q. J. Mech. App. Math., vol. 38, no. 2, pp. 323–341, 1985.
  35. G. Manara, A. Monorchio, and R. Reggiannini, “A space-time discretization criterion for a stable time-marching solution of the electric field integral equation,” IEEE Trans. Antennas Propag., vol. 45, no. 3, pp. 527–532, 1997.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now