Search search
submit Submit
Publication Date
to
Vol. 154
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
All Journals
PIER PIER B PIER C PIER M PIER Letters
2015-12-16
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
Brian Rautio,

    Dr. Brian Rautio

    Sonnet Software, North Syracuse

    USA

    Homepage

Vladimir I. Okhmatovski,

    Prof. Vladimir I. Okhmatovski

    University of Manitoba

    Canada

    Homepage

Jay Kyoon Lee

    Dr. Jay Kyoon Lee

    Department of Electrical Engineering and Computer Science

    Syracuse University

    USA

    Homepage

Progress In Electromagnetics Research, Vol. 154, 101-114, 2015
doi:10.2528/PIER15110201
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
Brian Rautio, Vladimir I. Okhmatovski, and Jay Kyoon 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
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.

Download Full Article (276) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.