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 Google Scholar

2. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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. Google Scholar

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 Google Scholar

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. Google Scholar

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. Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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 Google Scholar

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

25. Haynes, M. S., Waveport Scattering Library, Jet Propulsion Laboratory, 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, 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. Google Scholar

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

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 Google Scholar

Dr. Mark S. Haynes

Dr. Ines Fenni