volume | PIER Journals

Abstract

A compression algorithm for the T-matrix scattering solution from multiple objects and incident fields is derived and examined which we call the Compressed T-Matrix Algorithm (CTMA). The CTMA is derived by applying the SVD and Woodbury matrix-inverse identity to compress the original T-matrix system of equations and simultaneously compress the matrix of right-hand side incident field vectors. This is suited for scattering problems with many incident directions. We quantify the compression rates for different collections of dielectric spheres and draw comparisons to the Characteristic Basis Function Method (CBFM) with which the CTMA shares many structural similarities.

1. Waterman, P. C. and R. Truell, "Multiple scattering of waves," J. of Math. Phy., Vol. 2, No. 4, 512-537, 1961.
doi:10.1063/1.1703737

2. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, New York, 1995.

3. Mishchenko, M. I., G. Videen, V. A. Babenko, N. G. Khlebtsov, and T. Wriedt, "T-matrix theory of electromagnetic scattering by particles and its applications: A comprehensive reference database," J. Quant. Spectrosc. Radiat. Transfer, Vol. 88, No. 1-3, 357-406, 2004.
doi:10.1016/j.jqsrt.2004.05.002

4. Koc, S. and W. C. Chew, "Calculation of acoustical scattering from a cluster of scatterers," J. Acoust. Soc. Am., Vol. 103, No. 2, 721-734, 1998.
doi:10.1121/1.421231

5. Chew, W. C., L. Gurel, Y.-M. Wang, G. Otto, R. L. Wagner, and Q. H. Liu, "A generalized recursive algorithm for wave-scattering solutions in two dimensions," IEEE Trans. Microwave Theory and Techniques, Vol. 40, No. 4, 716-723, 1992.
doi:10.1109/22.127521

6. Wang, Y.-M. and W. Chew, "A recursive T-matrix approach for the solution of electromagnetic scattering by many spheres," IEEE Trans. Ant. Prop., Vol. 41, No. 12, 1633-1639, 1993.
doi:10.1109/8.273306

7. Chew, W. C., C. Lu, and Y. Wang, "Efficient computation of three-dimensional scattering of vector electromagnetic waves," JOSA A, Vol. 11, No. 4, 1528-1537, 1994.
doi:10.1364/JOSAA.11.001528

8. Chew, W. and C. Lu, "The recursive aggregate interaction matrix algorithm for multiple scatterers," IEEE Trans. on Ant. and Prop., Vol. 43, No. 12, 1483-1486, 1995.
doi:10.1109/8.475942

9. Gumerov, N. A. and R. Duraiswami, "Computation of scattering from N spheres using multipole reexpansion," J. Acoust. Soc. Am., Vol. 112, No. 6, 2688-2701, 2002.
doi:10.1121/1.1517253

10. Mackowski, D. W. and M. I. Mishchenko, "A multiple sphere T-matrix fortran code for use on parallel computer clusters," J. Quant. Spec. and Rad. Trans., Vol. 112, No. 13, 2182-2192, 2011.
doi:10.1016/j.jqsrt.2011.02.019

11. Egel, A., L. Pattelli, G. Mazzamuto, D. S. Wiersma, and U. Lemmer, "Celes: CUDA-accelerated simulation of electromagnetic scattering by large ensembles of spheres," J. Quant. Spec. and Rad. Trans., Vol. 199, 103-110, 2017.
doi:10.1016/j.jqsrt.2017.05.010

12. Siqueira, P. R. and K. Sarabandi, "T-matrix determination of effective permittivity for three-dimensional dense random media," IEEE Trans. Ant. Prop., Vol. 48, No. 2, 317-327, 2000.
doi:10.1109/8.833082

13. Maaskant, R., R. Mittra, and A. Tijhuis, "Fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm," IEEE Trans. Ant. Prop., Vol. 56, No. 11, 3440-3451, 2008.
doi:10.1109/TAP.2008.2005471

14. Um, J. and G. M. McFarquhar, "Optimal numerical methods for determining the orientation averages of single-scattering properties of atmospheric ice crystals," J. Quant. Spec. and Rad. Trans., Vol. 127, 207-223, 2013.
doi:10.1016/j.jqsrt.2013.05.020

15. Liao, D. and T. Dogaru, "Full-wave scattering and imaging characterization of realistic trees for FOPEN sensing," IEEE GRSL, Vol. 13, No. 7, 957-961, 2016.

16. Mittra, R. and K. Du, "Characteristic basis function method for iteration-free solution of large method of moments problems," Progress In Electromagnetics Research B, Vol. 6, 307-336, 2008.
doi:10.2528/PIERB08031206

17. Zhao, K., M. N. Vouvakis, and J.-F. Lee, "The adaptive cross approximation algorithm for accelerated method of moments computations of EMC problems," IEEE Trans. on Elec. Comp., Vol. 47, No. 4, 763-773, 2005.

18. Mackowski, D. W., "Analysis of radiative scattering for multiple sphere configurations," Proc. Roy. Soc., Ser. A, Math. and Phys. Sci., Vol. 433, No. 1889, 599-614, 1991.

19. Chew, W. C., "Recurrence relations for three-dimensional scalar addition theorem," Journal of Electromagnetic Waves and Applications, Vol. 6, No. 1-4, 133-142, 1992.
doi:10.1163/156939392X01075

20. Chew, W. C. and Y. Wang, "Efficient ways to compute the vector addition theorem," Journal of Electromagnetic Waves and Applications, Vol. 7, No. 5, 651-665, 1993.
doi:10.1163/156939393X00787

21. Yaghjian, A. D., "Sampling criteria for resonant antennas and scatterers," J. App. Phys., Vol. 79, No. 10, 7474-7482, 1996.
doi:10.1063/1.362683

22. Woodbury, M. A., Inverting Modified Matrices, Statistical Research Group, 1950.

23. Hager, W. W., "Updating the inverse of a matrix," SIAM Rev., Vol. 31, No. 2, 221-239, 1989.
doi:10.1137/1031049

24. Tsang, L., J. Kong, and K. Ding, Scattering of Electromagnetic Waves, Vol. 1: Theory and Applications, Wiley Interscience, New York, 2000.
doi:10.1002/0471224286

25. Haynes, M. S., Waveport Scattering Library, Jet Propulsion Laboratory, California Institute of Technology, 2021, https://doi.org/10.48588/JPL.HE9D-BA55, https://github.com/nasajpl/Waveport.

26. Peterson, A. F., S. L. Ray, and R. Mittra, Computational Methods for Electromagnetics, Vol. 2, IEEE Press, New York, 1998.

27. Fenni, I., Z. S. Haddad, H. Roussel, K.-S. Kuo, and R. Mittra, "A computationally efficient 3-D full-wave model for coherent EM scattering from complex-geometry hydrometeors based on MoM/CBFM-enhanced algorithm," IEEE TGRS, Vol. 56, No. 5, 2674-2688, 2017.

28. Brand, M., "Incremental singular value decomposition of uncertain data with missing values," Euro. Conf. Comp. Vis., 707-720, Springer, 2002.

29. Baker, C. G., K. A. Gallivan, and P. Van Dooren, "Low-rank incremental methods for computing dominant singular subspaces," Lin. Alg. App., Vol. 436, No. 8, 2866-2888, 2012.
doi:10.1016/j.laa.2011.07.018

Dr. Mark S. Haynes

Dr. Ines Fenni