Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-23T20:22:44.407Z Has data issue: false hasContentIssue false
  • English
  • Français

A Multilevel Numerical Approach with Application in Time-Domain Electromagnetics

Published online by Cambridge University Press:  24 March 2015

Avijit Chatterjee
Avijit Chatterjee*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Technology, Bombay, Mumbai 400076, India
*
*Corresponding author. Email address:[email protected] (A. Chatterjee)
Get access

Abstract

An algebraic multilevel method is proposed for efficiently simulating linear wave propagation using higher-order numerical schemes. This method is used in conjunction with the Finite Volume Time Domain (FVTD) technique for the numerical solution of the time-domain Maxwell’s equations in electromagnetic scattering problems. In the multilevel method the solution is cycled through spatial operators of varying orders of accuracy, while maintaining highest-order accuracy at coarser approximation levels through the use of the relative truncation error as a forcing function. Higher-order spatial accuracy can be enforced using the multilevel method at a fraction of the computational cost incurred in a conventional higher-order implementation. The multilevel method is targeted towards electromagnetic scattering problems at large electrical sizes which usually require long simulation times due to the use of very fine meshes dictated by point-per-wavelength requirements to accurately model wave propagation over long distances.

Keywords

35L0574J0578A45778A4576M12Finite volumetime-domainMaxwell’s equationsscatteringmultilevelhigher-order
Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 3 , March 2015 , pp. 703 - 720
Copyright
Copyright © Global-Science Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Hesthaven, J.S., Higher-order accurate methods in time-domain electromagnetics: A review, Adv. in Imaging and Electron Phys., 127(2003), 59–123.CrossRefGoogle Scholar
[2]Kabakian, A.V., Shankar, V. and Hall, W.F., Unstructured grid-based discontinuous Galerkin method for broadband electromagnetic simulations, J. Sci. Comput., 20(2004), 405–431.CrossRefGoogle Scholar
[3]Yee, K.S. and Chen, J.S., The finite-difference time domain (FDTD) and finite-volume time-domain (FVTD) methods in solving Maxwell’s equations, IEEE Trans. Antennas and Propagation, 45(1997), 354–363.CrossRefGoogle Scholar
[4]Manry, C.W., Broschat, S.L. and Schneider, J.B., Higher-order FDTD methods for large problems, ACES J., 10(1995), 17–29.Google Scholar
[5]Brandt, A., Multi-level adaptive solutions to boundary value problems, Math. Comp., 31(1977), 333–390.CrossRefGoogle Scholar
[6]Brandt, A., Guide to multigrid development, in Springer Lecture Notes in Mathematics 960, Springer-Verlag, Berlin 1982.Google Scholar
[7]Fidkowski, K.J., Oliver, T.A.. Lu, J. and Darmofal, D.L., p-Multigrid solution of higher-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations, J. Comp. Phys., 207(2005), 92–113.CrossRefGoogle Scholar
[8]Briggs, W.L., Henson, V. E. and McCormick, S.F., A Multigrid tutorial, 2nd edition, SIAM, 2000.CrossRefGoogle Scholar
[9]Taflove, A. and Umashankar, K.R., Review of FD-TD numerical modeling of electromagnetic wave scattering and radar cross section, Proc. of the IEEE, 77(1989), 682–699.CrossRefGoogle Scholar
[10]Wan, W.L. and Chan, T.F., A phase error analysis of multigrid methods for hyperbolic problems, SIAM J. Sci. Comput., 25(2003), 857–880.CrossRefGoogle Scholar
[11]Deore, N. and Chatterjee, A., A cell-vertex based multigrid solution of the time domain Maxwell’s equations, PIER B, 23(2010), 181–197.CrossRefGoogle Scholar
[12]Chatterjee, A. and Myong, R.-S., Efficient implementation of higher-order finite volume time domain method for electrically large scatterers, PIER B, 17(2009), 233–254.CrossRefGoogle Scholar
[13]Chima, R.V., Turkel, E. and Schaffer, S., Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations, AIAA Paper, 87–0602(1987).CrossRefGoogle Scholar
[14]Shu, C.W. and Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes, J. Comp. Phys., 77(1988), 439–471.CrossRefGoogle Scholar
[15]Shu, C. W. and Osher, S., Efficient implementation of essentially non-oscillatory shock-capturing schemes II, J. Comp. Phys., 83(1989), 32–78.CrossRefGoogle Scholar
[16]Chatterjee, A. and Shrimal, A., Essentially nonoscillatory finite volume scheme for electromagnetic scattering by thin dielectric coatings, AIAA J., 42(2004), 361–365.CrossRefGoogle Scholar
[17]Rao, S.M., Vechinski, D.A. and Sarkar, T.K., Infinite conducting cylinders: TDIE solution, in Time domain electromagnetics, Academic Press, 1999Google Scholar
[18]Shankar, V., Hall, W.F. and Mohammadian, A.H, A time-domain differential solver for electromagnetic scattering problems, Proceedings of the IEEE, 77(1989), 709–721.CrossRefGoogle Scholar
[19]Casper, J., Shu, C-W and Atkins, H.L., A comparison of two formulations for higher-order accurate essentially non-oscillatory schemes, ICASE report number 93–27, 1993.CrossRefGoogle Scholar