Progress In Electromagnetics Research B
ISSN: 1937-6472
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 27 > pp. 1-19


By A. G. Radwan, M. H. Bakr, and N. K. Nikolova

Full Article PDF (658 KB)

We present a novel approach for adjoint transient sensitivity analysis with respect to discontinuities with space-dependent materials exhibiting known distribution. Our approach integrates the Time Domain Transmission-Line-Modeling (TD-TLM) with the Adjoint Variable Method (AVM). Using only one extra TD-TLM simulation, the sensitivities of the observed response with respect to all the parameters of the Gaussian distribution are obtained. The accuracy of our sensitivity analysis approach is illustrated through a number of different 2D and 3D examples. Using the previous sensitivities, gradient-based optimization technique is applied to exploit in the location and profile of various inhomogeneous material Gaussian distribution for inverse problems. This method can be repeated for any continuous or discontinuous distributions that exist in electromagnetic imaging for space dependent materials like cancer detection.

A. G. Radwan, M. H. Bakr, and N. K. Nikolova, "Transient Adjoint Sensitivities for Discontinuities with Gaussian Material Distributions," Progress In Electromagnetics Research B, Vol. 27, 1-19, 2011.

1. Feehery, W. F., J. E. Tolsma, and P. I. Barton, "Efficiently sensitivity analysis of large-scale differential-algebraic systems," Applied Numerical Mathematics, Vol. 25, 41-54, 1997.

2. Cao, Y., S. Li, L. Petzold, and R. Serban, "Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution," SIAM J. Sci. Comput., Vol. 24, 1076-1089, 2003.

3. Li, S. and L. Petzold, "Adjoint sensitivity analysis for time-dependent partial differential equations with adaptive mesh refinement," Journal of Computational Physics, Vol. 198, 310-325, 2004.

4. Ding, J.-Y., Z.-K. Pan, and L.-Q. Chen, "Second order adjoint sensitivity analysis of multibody systems described by differential-algebraic equations," Multibody Syst. Dyn., Vol. 18, 599-617, 2007.

5. Errico, R. M., "What is an adjoint model?," Bulletin of the American Meteorological Society, Vol. 78, 2577-2591, 1997.

6. Vallese, L. M., "Incremental versus adjoint models for network sensitivity analysis," IEEE Trans. Circuits & Systems, Vol. 21, No. 1, 46-49, 1974.

7. Lee, H., "Adjoint variable method for structural design sensitivity analysis of a distinct eigenvalue problem," KSME International Journal, Vol. 13, No. 6, 470-476, 1999.

8. Chung, Y.-S., J. Ryu, C. Cheon, I. H. Park, and S.-Y. Hahn, "Optimal design method for microwave devices using time domain method and design sensitivity analysis --- Part I: FETD case," IEEE Trans. on Magnetics, Vol. 37, No. 5, 3289-3293, Sep. 2001.

9. Webb, J. P., "Design sensitivity of frequency response in 3D finite-element analysis of microwave devices," IEEE Trans. Magnetics, Vol. 38, 1109-1112, 2002.

10. Basl, P. A. W., M. H. Bakr, and N. K. Nikolova, "The theory of self-adjoint S-parameter sensitivities for lossless nonhomogeneous TLM problems," IET Microw. Antennas Propagation, Vol. 2, No. 3, 211-220, 2008.

11. Drogoudis, D. G., G. A. Kyriacou, and J. N. Sahalos, "Microwave tomography employing an adjoint network based sensitivity matrix," Progress In Electromagnetics Research, Vol. 94, 213-242, 2009.

12. Chung, Y. S., C. Cheon, I. H. Park, and S. Y. Hahn, "Optimal design method for microwave device using time domain method and design sensitivity analysis --- Part II: FDTD case," IEEE Trans. Magn., Vol. 37, 3255-3259, Sep. 2001.

13. Bakr, M. H. and N. K. Nikolovac, "An adjoint method for time domain transmission-line-modeling with fixed structured grids," IEEE Trans. Microwave Theory Tech., Vol. 52, 554-559, Feb. 2004.

14. Bakr, M. H. and N. K. Nikolova, "An adjoint variable method for time domain TLM with wide-band John matrix boundaries," IEEE Trans. Microwave Theory Tech., Vol. 52, 678-685, 2004.

15. Nikolova, N. K., H. W. Tam, and M. H. Bakr, "Sensitivity analysis with the FDTD method on structured grids," IEEE Trans. Microwave Theory Tech., Vol. 52, No. 4, 1207-1216, Apr. 2004.

16. Nikolova, N. K., Y. Li, and M. H. Bakr, "Sensitivity analysis of scattering parameters with electromagnetic time-domain simulators," IEEE Trans. Microwave Theory Tech., Vol. 54, No. 4, 1598-1610, Apr. 2006.

17. Song, Y., Y. Li, N. K. Nikolova, and M. H. Bakr, "Self-adjoint sensitivity analysis of lossy dielectric structures with electromagnetic time domain simulators," Int. J. Numer. Model., Vol. 21, 117-132, Oct. 2007.

18. Bakr, M. H., P. Zhao, and N. K. Nikolova, "Adjoint first order sensitivities of time domain responses and their applications in solution of inverse problems," IEEE Trans. Antennas Propagat., Jul. 2009.

19. Ozyurt, B. D. and P. I. Barton, "Large-scale dynamic optimization using the directional second-order adjoint method," Ind. Eng. Chem. Res., Vol. 44, 1804-1811, 2005.

20. Georgieva, N. K., S. Glavic, M. H. Bakr, and J. W. Bandler, "Feasible adjoint sensitivity technique for EM design optimization," IEEE Trans. Microwave Theory Tech., Vol. 50, 2751-2758, Dec. 2002.

21. Nikolova, N. K., R. Safian, E. A Soliman, and M. H. Bakr, "Accelerated gradient based optimization using adjoint sensitivities," IEEE Trans. Antennas Propagat., Vol. 52, 2147-2157, Aug. 2004.

22. Goharian, M., M. Soleimani, and G. R. Moran, "A trust region subproblem for 3D electrical impedance tomography inverse problem using experimental data," Progress In Electromagnetics Research, Vol. 94, 19-32, 2009.

23. Mojabi, M. and J. LoVetri, "Adapting the normalized cumulative periodogram parameter-choice method to the Tikhonov regularization of 2-D/TM electromagnetic inverse scattering using Born iterative method," Progress In Electromagnetics Research, Vol. 1, 111-138, 2008.

24. Yu, C., M. Yuan, and Q. H. Liu, "Reconstruction of 3D objects from multi-frequency experimental data with a fast DBIM-BCGS method," Inverse Problems, 25, doi:10.1088/0266-5611/25/2/024007, 2009.

25. Bindu, G., A. Lonappan, V. Thomas, C. K. Aanandan, K. T. Mathew, and S. J. Abraham, "Active microwave imaging for breast cancer detection," Progress In Electromagnetics Research, Vol. 58, 149-169, 2006.

26. Johns, P. B. and R. L. Beurle, "Numerical modeling of 2-dimensional scattering problems using a transmission line matrix," Proceedings of IEE, Vol. 118, No. 9, 1203-1208, Sep. 1971.

27. Christopoulos, C., The Transmission-line-method TLM, IEEE Press, 1995.

28. Matlab, Version 7.0.1, , 2004.

© Copyright 2010 EMW Publishing. All Rights Reserved