Abstract
Inverse scattering is a systematic approach to nondestructive testing, geophysical prospecting, remote sensing, and medical imaging. Being both nonlinear and ill-posed, inverse scattering problems are among the most challenging in computational science. In this chapter we expose the intimate connection between these problems and reduced-order modeling techniques, which allow significant reduction in computational complexity and efforts. Exploiting the natural symmetries of the electromagnetic field equations we develop and analyze reduced-order models for the parametric inversion problems arising in effective medium theory, metamaterials, and photonics. These models are Padé approximations of the measured scattered field. The achieved significant computational gain allows us to solve these large numerical problems by simple inspection of a two-dimensional objective functional.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P. J. Antsaklis, A. N. Michel, Linear Systems, (Birkhäuser, Boston, 2006).
C. Balanis, Antenna Theory - Analysis and Design, (John Wiley and Sons, New York, 1982).
H. Benisty, V. Berger, J.-M. Gerard, D. Maystre, A. Tchelnokov, Photonic Crystals, (Springer, 2005).
N. V. Budko, R. F. Remis, Inverse Problems 20, 2004, pp. S17–S26.
N. V. Budko, A. B. Samokhin, SIAM Journal on Scientific Computing 28, 2006, pp. 682–700.
W. C. Chew, J. M. Jin, E. Michielssen, J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, (Artech House, Norwood, 2001).
V. L. Druskin, L. A. Knizhnerman, USSR Computational Mathematics and Mathematical Physics 29, 1989, pp. 112–121.
V. Druskin, M. Zaslavsky, Inverse Problems 23, 2007, pp. 1599–1610.
P. Feldman, R. W. Freund, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 14, 1995, pp. 639–649.
A. Frommer, U. Glässner, SIAM Journal on Scientific Computing 19, 1998, pp. 15–26.
A. Frommer, P. Maas, SIAM Journal on Scientific Computing 20, 1999, pp. 1831–1850.
G. H. Golub, Z. Strakos, Numerical Algorithms 8, 1994, pp. 241–268.
J. D. Joannopoulos, R. D. Meade, J. N. Winn, Photonic Crystals, (Princeton Univ. Press, 1995).
C. M. Krowne, Y. Zhang (editors), Physics of Negative Refraction and Negative Index Materials, (Springer, 2007).
R. Liu, T. J. Cui, D. Huang, B. Zhao, D. R. Smith, Phys. Rev. E 76(2), 2007, 026606.
J. B. Pendry, Phys. Rev. Lett. 85, 2000, pp. 3966–3969.
R. F. Remis, PIERS Online 2, 2006, pp. 206– 209.
R. F. Remis, N. V. Budko, Proceedings ICEAA05 and EESC05, 2005, pp. 409–412.
D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, S. Schultz, Phys. Rev. Lett. 84, 2000, pp. 4184–4187.
H. A. van der Vorst, Iterative Krylov Methods for Large Linear Systems, (Cambridge University Press, Cambridge, 2003).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Remis, R.F., Budko, N.V. (2009). A Model-Order Reduction Approach to Parametric Electromagnetic Inversion. In: Koren, B., Vuik, K. (eds) Advanced Computational Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 71. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03344-5_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-03344-5_1
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03343-8
Online ISBN: 978-3-642-03344-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)