Search search
submit Submit
Publication Date
to
Vol. 95
Latest Volume
All Volumes
PIER 180 [2024] 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
2009-08-06
An Efficient Approach for Multifrontal Algorithm to Solve Non-Positive-Definite Finite Element Equations in Electromagnetic Problems
By
Jin Tian,

    Dr. Jin Tian

    School of Electronic Engineering

    Xidian University

    China

    Homepage

Zhi-Qing Lv,

    Dr. Zhi-Qing Lv

    Xidian University

    China

    Homepage

Xiao-Wei Shi,

    Professor Xiao-Wei Shi

    School of Electronics Engineering

    Xidian University

    China

    Homepage

Le Xu,

    Dr. Le Xu

    Xidian University

    China

    Homepage

Feng Wei

    Prof. Feng Wei

    Xidian University

    China

    Homepage

Progress In Electromagnetics Research, Vol. 95, 121-133, 2009
doi:10.2528/PIER09070207
Abstract
A new method called Expanded Cholesky Method (ECM) is proposed in this paper. The method can be used to decompose sparse symmetric non-positive-definite finite element (FEM) matrices. There are some advantages of the ECM, such as low storage, simplicity and easy parallelization. Based on the method, multifrontal (MF) algorithm is applied in non-positive-definite FEM computation. Numerical results show that the hybrid ECM/MF algorithm is stable and effective. In comparison with Generalized Minimal Residual Method (GMRES) in FEM electromagnetic computation, hybrid ECM/MF technology has distinct advantages in precision. The proposed method can be used to calculate a class of non-positive-definite electromagnetic problems.
Citation
Jin Tian, Zhi-Qing Lv, Xiao-Wei Shi, Le Xu, and Feng Wei, "An Efficient Approach for Multifrontal Algorithm to Solve Non-Positive-Definite Finite Element Equations in Electromagnetic Problems," Progress In Electromagnetics Research, Vol. 95, 121-133, 2009.
doi:10.2528/PIER09070207
References

1. Jianmin, J., "The finite element method in electromagnetics," The Finite Element Method in Electromagnetics.

2. Zhang, J. J., Y. Luo, S. Xi, H. Chen, L.-X. Ran, B.-I. Wu, and J. A. Kong, "Directive emission obtained by coordinate transformation," Progress In Electromagnetics Research, Vol. 81, 437-446, 2008.
doi:10.2528/PIER08011002

3. Soleimani, M., C. N. Mitchell, R. Banasiak, R. Wajman, and A. Adler, "Four-dimensional electrical capacitance tomography imaging using experimental data," Progress In Electromagnetics Research, Vol. 90, 171-186, 2009.
doi:10.2528/PIER09010202

4. Ozgun, O. and M. Kuzuoglu, "Finite element analysis of electromagnetic scattering problems via iterative leap-field domain decomposition method," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 2--3, 251-266, 2008.
doi:10.1163/156939308784160668

5. Hu, J. X. and B. D. Ge, "Study on conformal FDTD for electromagnetic scattering by targets with thin coating," Progress In Electromagnetics Research, Vol. 79, 305-319, 2008.
doi:10.2528/PIER07101902

6. Kalaee, P. and J. Rashed-Mohassel, "Investigation of dipole radiation pattern above a chiral media using 3D BI-FDTD approach," Journal of Electromagnetic Waves and Applications, Vol. 23, No. 1, 75-86, 2009.
doi:10.1163/156939309787604706

7. Liu, H. and H. W. Yang, "FDTD analysis of magnetized ferrite sphere," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 17--18, 2399-2406, 2008.
doi:10.1163/156939308787543787

8. Swillam, M. A. and M. H. Bakr, "Full wave sensitivity analysis of guided wave structures using FDTD," Journal of Electromagnetic Waves and Applications, Vol. 22, No. 16, 2135-2145, 2008.
doi:10.1163/156939308787522474

9. Dehdasht-Heydari, R., H. R. Hassani, R. A. Mallahzadeh, and , "A new 2--18 GHz quad-ridged horn antenna," Progress In Electromagnetics Research, Vol. 81, 183-195, 2008.
doi:10.2528/PIER08010103

10. Kasabegouda, V. G. and J. K. Vinoy, "Broadband suspended microstrip antenna for circular polarization," Progress In Electromagnetics Research, Vol. 90, 353-368, 2009.
doi:10.2528/PIER09012901

11. Carpentieri, B., "Fast iterative solution methods in electromagnetic scattering," Progress In Electromagnetics Research, Vol. 79, 151-178, 2008.
doi:10.2528/PIER07100802

12. Zhao, L., T. J. Cui, and W. D. Li, "An efficient algorithm for EM scattering by electrically large dielectric objects using MR-QEB iterative scheme and CG-FFT method," Progress In Electromagnetics Research, Vol. 67, 67-341, 2009.

13. Babolian, E., Z. Masouri, and S. Hatamzadeh-Varmazyar, "NEW direct method to solve nonlinear volterra-fredholm integral and integro-di®erential equations using operational matrix with block-pulse functions ," Progress In Electromagnetics Research B, Vol. 8, 59-76, 2008.
doi:10.2528/PIERB08050505

14. Schreiber, R., "A new implementation of sparse Gaussian elimination," ACM Transactions on Mathematical Software , Vol. 8, 256-276, 1982.
doi:10.1145/356004.356006

15. Duff, S. I. and K. J. Reid, "The multifrontal solution of indefinite sparse symmetric linear equations," ACM Transactions on Mathematical Software, Vol. 9, 302-325, 1983.
doi:10.1145/356044.356047

16. Chen, R. S., D. X. Wang, E. K. N. Yung, and J. M. Jin, "Application of the multifrontal method to the vector FEM for analysis of microwave filters," MOTL, Vol. 31, 465-470, 2001.
doi:10.1002/mop.10064

17. Hao, X. S., Theoretical Research and Implementation of Technology of Multifrontal Method, Solid Mechanics, 2003.

18. Liu, J., "The multifrontal method for sparse matrix solution: Theory and practice," SIAM Review, 82-109, 1992.
doi:10.1137/1034004

19. Zhuang, W., X. P. Feng, L. Mo, and R. S. Chen, "Multifrontal method preconditioned sparse-matrix/canonical grid algorithm for fast analysis of microstrip structure," APCP, 2005.

20. Wiping, Y., Numerical Analysis, Southeast University Press, 1992.

21. George, A. and J. W. Liu, Computer Solution of Large Sparse Positive Definite, Prentice Hall Professional Technical Reference, 1981.

22. Ashcraft, C. and J. Liu, "Generalized nested dissection: Some recent progress," Proceedings of Fifth SIAM Conference on Applied Linear Algebra, Snowbird, Utah, 1994.

23. Amestoy, P. R., A. T. Davis, and I. S. Duff, "An approximate minimum degree ordering algorithm," SIAM Journal on Matrix Analysis and Applications, Vol. 17, 886-905, 1996.
doi:10.1137/S0895479894278952

24. Liu, J., "The role of elimination trees in sparse factorization," SIAM Journal on Matrix Analysis and Applications, Vol. 11, 134, 1990.
doi:10.1137/0611010

Download Full Article (336) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.