Search search
submit Submit
Publication Date
to
Vol. 90
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
2009-02-10
A Generalized GPS Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix
By
Qing Wang,

    Dr. Qing Wang

    National Key Laboratory of Antenna and Microwave Technology

    Xidian University

    China

    Homepage

Yu-Chun Guo,

    Dr. Yu-Chun Guo

    Antenna Research Department

    Jiangnan Electronic Communication Research Institute

    China

    Homepage

Xiao-Wei Shi

    Professor Xiao-Wei Shi

    School of Electronics Engineering

    Xidian University

    China

    Homepage

Progress In Electromagnetics Research, Vol. 90, 121-136, 2009
doi:10.2528/PIER09010512
Abstract
A generalized GPS (GGPS) algorithm is proposed for the problem of reducing the bandwidth and profile of the stiffness matrix in finite element problems. The algorithm has two key-points. Firstly and most importantly, more pseudo-peripheral nodes are found, used as the origins for generating more level structures, rather than only two level structures in the GPS (Gibbs-Poole-Stockmeyer) algorithm. A new level structure is constructed with all the level structures rooted at the pseudo-peripheral nodes, leading to a smaller level width than the level width of any level structure's in general. Secondly, renumbering by degree is changed to be sum of the adjacent nodes codes to make a better renumbering in each level. Simulation results show that the GGPS algorithm can reduce the bandwidth by about 37.63% and 8.91% and the profiles by 0.17% and 2.29% in average for solid models and plane models, respectively, compared with the outcomes of GPS algorithm. The execution time is close to the GPS algorithm. Empirical results show that the GGPS is superior to the GPS in reducing bandwidth and profile.
Citation
Qing Wang, Yu-Chun Guo, and Xiao-Wei Shi, "A Generalized GPS Algorithm for Reducing the Bandwidth and Profile of a Sparse Matrix," Progress In Electromagnetics Research, Vol. 90, 121-136, 2009.
doi:10.2528/PIER09010512
References

1. Wang, Q., Q., Y. C. Guo, and X. W. Shi, "An improved matrix bandwidth and profile reduction algorithm in FEM problems," Progress In Electromagnetics Research Symposium, Hangzhou, China, 2008.

2. Amjadi, S. M. and M. Soleimani, "Design of band-pass waveguide filter using frequency selective surfaces loaded with surface mount capacitors based on split-field update FDTD method," Progress In Electromagnetics Research B, Vol. 3, 271-281, 2008.
doi:10.2528/PIERB07122402

3. Zhou, X. and G. W. Pan, "Application of physical spline finite element method (PSFEM) to fullwave analysis of waveguides ," Progress In Electromagnetics Research, PIER 60, 19-41, 2006.

4. Wei, X. C., E. P. Li, and Y. J. Zhang, "Application of the improved finite element-fast multipole method on large scattering problems," Progress In Electromagnetics Research, PIER 47, 49-60, 2004.

5. Doncker, P. D., "The use of tansfinite elements in the methods of moments applied to electromagnetic scattering by dielectric cylinders," Progress In Electromagnetics Research, PIER 25, 77-94, 2000.

6. Bedrosian, G., "High-performance computing for finite element methods in low-frequency electromagnetics," Progress In Electromagnetics Research, PIER 07, 57-110, 1993.

7. Vaish, A. and H. Parthasarathy, "Analysis of a rectangular waveguide using finite element method," Progress In Electromagnetics Research C, Vol. 2, 117-125, 2008.
doi:10.2528/PIERC08031801

8. Hernandez, L. M. A. and M. G. Quintillan, "A finite element method code to analyse waveguide dispersion," Journal of Electromagnetic Waves and Applications, Vol. 21, No. 3, 397-408, 2007.
doi:10.1163/156939307779367396

9. Jin, J. M., The Finite Element Method in Electromagnetics, Wiley, New York, 2002.

10. Cuthill, E. and J. Mckee, "Reducing the bandwidth of sparse symmetric matrices," Proceedings of the 1969 24th National Conference, 157-172, 1969.
doi:10.1145/800195.805928

11. Reid, J. K. and J. A. Scott, "Implementing Hager's exchange methods for matrix profile reduction," ACM Transcations on Mathematical Software, Vol. 28, No. 4, 377-391, 2002.
doi:10.1145/592843.592844

12. Chan, W. M. and A. George, "A lineartime implementation of the reverse Cuthill-McKee algorithm," BIT Numerical Mathematics, Vol. 20, No. 1, 8-14, 1980.
doi:10.1007/BF01933580

13. Gibbs, N. E., "Algorithm 509: A hybrid profile reduction algorithm [F1]," ACM Transactions on Mathematical Software, Vol. 2, No. 4, 378-387, 1976.
doi:10.1145/355705.355713

14. Gibbs, N. E., W. G. Poole, Jr., and P. K. Stockmeyer, "An algorithm for reducing the bandwidth and profile of a sparse matrix," SIAM Journal on Numerical Analysis, Vol. 13, No. 2, 236-250, 1976.
doi:10.1137/0713023

15. George, A. and J. W. H. Liu, "An implementation of a pseudoperipheral node finder," ACM Transactions on Mathematical Software, Vol. 5, No. 3, 284-295, 1979.
doi:10.1145/355841.355845

16. Souza, L. T. and D. W. Murray, "An alternative pseudoperipheral node finder for resequencing schemes," International Journal for Numerical Methods in Engineering, Vol. 36, No. 19, 3351-3379, 1993.
doi:10.1002/nme.1620361910

17. Tai, C. C. and Y. L. Pan, "Finite element method simulationof photoinductive imaging for cracks," Progress In Electromagnetics Research Letters, Vol. 2, 53-61, 2008.
doi:10.2528/PIERL07122807

18. Boutora, Y., N. Takorabet, R. Ibtiouen, and S. Mezani, "A new method for minimizing the bandwidth and profile of square matrices for triangular finite elements mesh," IEEE Transactions on Magnetics, Vol. 43, No. 4, 1513-1516, 2007.
doi:10.1109/TMAG.2007.891460

Download Full Article (356) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.