PIER
 
Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
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THE UNIFED-FFT GRID TOTALIZING ALGORITHM FOR FAST O(N LOG N) METHOD OF MOMENTS ELECTROMAGNETIC ANALYSIS WITH ACCURACY TO MACHINE PRECISION (Invited Paper)

By B. Rautio, V. I. Okhmatovski, and J. K. Lee

Full Article PDF (853 KB)

Abstract:
While considerable progress has been made in the realm of speed-enhanced electromagnetic (EM) solvers, these fast solvers generally achieve their results through methods that introduce additional error components by way of geometric type approximations, sparse-matrix type approximations, multilevel type decomposition of interactions, and assumptions regarding the stochastic nature of EM problems. This work introduces the O(N logN) Uni ed-FFT grid totalizing (UFFT-GT) method, a derivative of method of moments (MoM), which achieves fast analysis with minimal to zero reduction in accuracy relative to direct MoM solution. The method uniquely combines FFT-enhanced Matrix Fill Operations (MFO) that are calculated to machine precision with FFT-enhanced Matrix Solve Operations (MSO) that are also calculated to machine precision, for an expedient solution that does not compromise accuracy.

Citation:
B. Rautio, V. I. Okhmatovski, and J. K. Lee, "The Unifed-FFT Grid Totalizing Algorithm for Fast O(n Log n ) Method of Moments Electromagnetic Analysis with Accuracy to Machine Precision (Invited Paper)," Progress In Electromagnetics Research, Vol. 154, 101-114, 2015.
doi:10.2528/PIER15110201
http://www.jpier.org/PIER/pier.php?paper=15110201

References:
1. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving largescale electromagnetic scattering and radiation problems," Radio Science, Vol. 31, No. 5, 1225-1251, Sep.-Oct. 1996.
doi:10.1029/96RS02504

2. Coifman, R., V. Rokhlin, and S. Wandzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., Vol. 35, No. 3, 712, Jun. 1993.
doi:10.1109/74.250128

3. Sonnet emSuite Version 14, , Sonnet Software, North Syracuse, NY, 2013.

4. Rautio, J. C., "An ultra-high precision benchmark for validation of planar electromagnetic analyses," IEEE Trans. on Microw. Theory Tech., Vol. 42, No. 11, 2046-2050, Nov. 1994.
doi:10.1109/22.330117

5. Rautio, B. J., V. I. Okhmatovski, A. C. Cangellaris, J. C. Rautio, and J. K. Lee, "The unified-FFT algorithm for fast electromagnetic analysis of planar integrated circuits printed on layered media inside a rectangular enclosure," IEEE Trans. on Microw. Theory Tech., Vol. 62, No. 5, 1112-1121, May 2014.
doi:10.1109/TMTT.2014.2315594

6. Catedra, M. F., R. F. Torres, J. Basterrechea, and E. Gago, The CG-FFT Method - Application of Signal Processing Techniques to Electromagnetics, Artech House, Norwood, MA, 1995.

7. Morsey, J. D., "Integral equation methodologies for the signal integrity analysis of PCB and interconnect structures in layered media from DC to multi-GHz frequencies,", Ph.D. Dissertation, Clemson Univ., Clemson, SC., 2003.

8. Morsey, J. D., V. I. Okhmatovski, and A. C. Cangellaris, "Finite-thickness conductor models for full-wave analysis of interconnects with a fast integral equation method," IEEE Adv. Packag., Vol. 27, No. 1, 24-33, Feb. 2004.
doi:10.1109/TADVP.2004.825459

9. Yang, K. and A. E. Yilmaz, "An FFT-accelerated integral-equation solver for analyzing scattering in rectangular cavities," IEEE Trans. on Microw. Theory Tech., Vol. 62, No. 9, 1930-1942, Sep. 2014.
doi:10.1109/TMTT.2014.2335176

10. Saad, Y., Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, 2003.
doi:10.1137/1.9780898718003

11. Taboada, J. M., M. G. Araujo, F. O. Basterio, J. L. Rodriguez, and L. Landesa, "MLFMA-FFT parallel algorithm for the solution of extremely large problems in electromagnetics," Proc. of the IEEE, Vol. 101, No. 2, 350-363, Jan. 2013.
doi:10.1109/JPROC.2012.2194269

12. Dang, V., Q. M. Nguyen, and O. Kilic, "GPU cluster implementation of FMM-FFT for large-scale electromagnetic problems," IEEE Antennas Wireless Propag. Lett., Vol. 13, 1259-1262, Jun. 2014.
doi:10.1109/LAWP.2014.2332972

13. Sheng, F. and D. Jiao, "A deterministic-solution based fast eigenvalue solver with guaranteed convergence for finite-element based 3-D electromagnetic analysis," IEEE Trans. Antennas Propag., Vol. 61, No. 7, 3701-3711, Jul. 2013.
doi:10.1109/TAP.2013.2258315

14. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Norwood, MA, 2001.

15. Harrington, R. F., Time-harmonic Electromagnetic Fields, McGraw-Hill Co., New York, NY, 1961.

16. Smith, C. F., A. F. Peterson, and R. Mittra, "The biconjugate gradient method for electromagnetic scattering," IEEE Trans. Antennas Propag., Vol. 38, No. 6, 938-940, Jun. 1990.
doi:10.1109/8.55595

17. Golub, G. H. and C. F. van Loan, Toeplitz and Related Systems, Matrix Computations, 3rd Ed., Ch. 4, Sec. 7, 193-205, Johns Hopkins Univ. Press, Baltimore, MD, 1996.

18. MATLAB, , MathWorks, Natick, MA, 2012.

19. SonnetLab Toolbox, , Sonnet Software, North Syracuse, NY, 2013.

20. Rautio, B. J., V. I. Okhmatovski, and J. K. Lee, "Fast 3D planar electromagnetic analysis via unified-FFT method," IEEE MTT-S Int. Symp. Dig., 1-3, Seattle, WA, Jun. 2-7, 2013.

21. Miyazawa, N., "Device having interdigital capacitor,", U.S. Patent 6 949 811, Sep. 27, 2005.

22. Rautio, B. J., Q. Long, A. Agrawal, and M. A. El Sabbagh, "Simulation geometry rasterization for applications toward graphene interconnect characterization," Proc. IEEE Intl. Symp. on Electromag. Compat., 406-410, Pittsburgh, PA, Aug. 6-10, 2012.


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