Vol. 105
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]
2010-06-02
MLFMA-FFT Parallel Algorithm for the Solution of Large-Scale Problems in Electromagnetics (Invited Paper)
By
Progress In Electromagnetics Research, Vol. 105, 15-30, 2010
Abstract
An efficient hybrid MPI/OpenMP parallel implementation of an innovative approach that combines the Fast Fourier Transform (FFT) and the Multilevel Fast Multipole Algorithm (MLFMA) has been successfully used to solve an electromagnetic problem involving 620 millions of unknowns. The MLFMA-FFT method can deal with extremely large problems due to its high scalability and its reduced computational complexity. The former is provided by the use of the FFT in distributed calculations and the latter by the application of the MLFMA in shared computation.
Citation
Jose Taboada, Marta Gomez Araujo, Jose Manuel Bertolo, Luis Landesa, Fernando Obelleiro, and Jose Luis Rodriguez, "MLFMA-FFT Parallel Algorithm for the Solution of Large-Scale Problems in Electromagnetics (Invited Paper)," Progress In Electromagnetics Research, Vol. 105, 15-30, 2010.
doi:10.2528/PIER10041603
References

1. Harrington, R. F., Field Computation by Moment Method, IEEE Press, New York, 1993.

2. Coifman, R., V. Rokhlin, and S. Wanzura, "The fast multipole method for the wave equation: A pedestrian prescription," IEEE Antennas Propagat. Mag., Vol. 35, No. 3, 7-12, Jun. 1993.
doi:10.1109/74.250128

3. Song, J. M. and W. C. Chew, "Multilevel fast multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microw. Opt. Tech. Lett., Vol. 10, 14-19, Sep. 1995.
doi:10.1002/mop.4650100107

4. Song, J. M., C. C. Lu, W. C. Chew, and S. W. Lee, "Fast Illinois solver code (FISC)," IEEE Antennas Propag. Mag., Vol. 40, No. 3, 27-34, Jun. 1998.
doi:10.1109/74.706067

5. Velamparambil, S., J. M. Song, W. C. Chew, and K. Gallivan, "Scaleme: A portable scaleable multipole engine for electromagnetic and acoustic integral equation solvers," IEEE Antennas Propag. Soc. Int. Symp., Vol. 3, 1774-1777, Jun. 1998.

6. Velamparambil, S., J. E. Schutt-Aine, J. G. Nickel, J. M. Song, and W. C. Chew, "Solving large scale electromagnetic problems using a linux cluster and parallel MLFMA," IEEE Antennas Propag. Soc. Int. Symp., Vol. 1, 636-639, 1999.

7. Velamparambil, S., W. C. Chew, and M. L. Hastriter, "Scalable electromagnetic scattering computations," IEEE Antennas Propag. Soc. Int. Symp., Vol. 3, 176-179, 2002.

8. Velamparambil, S., W. C. Chew, and J. M. Song, "10 Million unknowns: Is it that big?," IEEE Antennas Propagat. Mag., Vol. 45, No. 3, 43-58, Apr. 2003.
doi:10.1109/MAP.2003.1203119

9. Sylvand, G., "Performance of a parallel implementation of the FMM for electromagnetics applications," Int. J. Numer. Meth. Fluids, Vol. 43, 865-879, 2003.

10. Velamparambil, S. and W. C. Chew, "Analysis and performance of a distributed memory multilevel fast multipole algorithm," IEEE Trans. Antennas Propag., Vol. 53, No. 8, 2719-2727, 2005.
doi:10.1109/TAP.2005.851859

11. Gurel, L. and O. Ergul, "Fast and accurate solutions of extremely large integral-equation problems discretised with tens of millions of unknowns," Electronics Letters, Vol. 43, No. 9, 499-500, Apr. 2007.
doi:10.1049/el:20070639

12. Ergul, O and L. Gurel, "Parallel-MLFMA solution of CFIE discretized with tens of millions of unknowns," Proc. 2nd Europ. Conf. Antennas Propag. (EuCAP), Nov. 2007.

13. Pan, X.-M. and X. X.-Q. Sheng, "A sophisticated parallel MLFMA for scattering by extremely large targets," IEEE Antennas Propagat. Mag., Vol. 50, 129-138, Jun. 2008.
doi:10.1109/MAP.2008.4563583

14. Ergul, O and L. Gurel, "Efficient parallelization of the multilevel fast multipole algorithm for the solution of large-scale scattering by extremely large targets," IEEE Antennas Propagat. Mag., Vol. 50, 129-138, Aug. 2008.

15. Ergul, O. and L. Gurel, "A hierarchical partitioning strategy for an e±cient parallelization of the multilevel fast multipole algorithm," IEEE Trans. Antennas Propag., Vol. 57, No. 6, 1740-1750, Jun. 2009.
doi:10.1109/TAP.2009.2019913

16. Wagner, R., J. M. Song, and W. C. Chew, "Montecarlo simulation of electromagnetic scattering from two-dimensional random rough surfaces ," IEEE Trans. Antennas Propag., Vol. 45, No. 2, 235-245, Feb. 1997.
doi:10.1109/8.560342

17. Waltz, C., K. Sertel, M. A. Carr, B. C. Usner, and J. L. Volakis, "Massively parallel fast multipole method solutions of large electromagnetic scattering problems," IEEE Trans. Antennas Propag., Vol. 55, No. 6, 1810-1816, Jun. 2007.
doi:10.1109/TAP.2007.898511

18. Landesa, L., J. M. Taboada, F. Obelleiro, J. L. Rodriguez, C. Mourino, and A. Gomez, "Solution of very large integral-equation problems with single-level FMM," Microw. Opt. Technol. Lett., Vol. 51, No. 6, 20-28, Dec. 2009.

19. Taboada, J. M., L. Landesa, F. Obelleiro, J. L. Rodriguez, J. M. Bertolo, M. G. Araujo, J. C. Mourino, and A. Gomez, "High scalability FMM-FFT electromagnetic solver for supercomputer systems," IEEE Antennas Propagat. Mag., Vol. 51, No. 6, 20-28, Dec. 2009.
doi:10.1109/MAP.2009.5433091

20. Taboada, J. M., L. Landesa, J. M. Bertolo, F. Obelleiro, J. L. Rodriguez, C. Mourino, and A. Gomez, "High scalablity multipole method for the analysis of hundreds of millions of unknowns," Proc. IEEE Europ. Conf. Antennas Propag. (EuCAP), Berlin, Germany, Mar. 2009.

21. Landesa, L., J. M. Taboada, J. L. Rodriguez, F. Obelleiro, J. M. Bertolo, J. C. Mourino, and A. Gomez, "Analysis of 0.5 billion unknowns using a parallel FMMFFT solver," Proc. IEEE Antennas Propag. Soc. Int. Symp., Charleston (South Carolina), USA, Jun. 2009.

22. Araujo, M. G., J. M. Taboada, F. Obelleiro, J. M. Bertolo, L. Landesa, J. Rivero, and J. L. Rodrguez, "Supercomputer aware approach for the solution of challenging electromagnetic problems," Progress In Electromagnetics Research, Vol. 101, 241-256, 2010.
doi:10.2528/PIER09121007

23. Saad, Y. and M. Schultz, "GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems," SIAMJ. Sci. Statist. Comput., Vol. 7, 856-869, 1986.
doi:10.1137/0907058

24. Gumerov, N. A., R. Duraiswami, and E. A. Borovikov, "Data structures, optimal choice of parameters and complexity results for generalized multilevel fast multipole methods in d dimensions ," UM Computer Science Technical Report CS-TR-4458 UMIACS, University of Maryland, 2003.

25. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propagat., Vol. 30, 409-418, May 1982.
doi:10.1109/TAP.1982.1142818

26. Knott, E. F., J. F. Shaeffer, and M. T. Tuley, Radar Cross Section, Artech House, Inc., Norwood, MA, 1985.