Vol. 143
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]
2013-11-18
A New 2D Non-Spurious Discontinuous Galerkin Finite Element Time Domain (DG-FETD) Method for Maxwell's Equations
By
Progress In Electromagnetics Research, Vol. 143, 385-404, 2013
Abstract
A new discontinuous Galerkin Finite Element Time Domain (DG-FETD) method for Maxwell's equations is developed. It can suppress spurious modes using basis functions based on polynomials with the same order of interpolation for electric field intensity and magnetic flux density (EB scheme). Compared to FETD based on EH scheme, which reqires different orders of interpolation polynomials for electric and magnetic field intensities, this method uses fewer unknowns and reduces the computation load. The discontinuous Galerkin method is employed to implement domain decomposition for the EB scheme based FETD. In addition, a well-posed time-domain perfectly matched layer (PLM) is extended to the EB scheme to simulate the unbounded problem. Leap frog method is utilized for explicit time stepping. Numerical results demonstrate that the above proposed methods are effective and efficient for 2D time domain TMz multi-domain problems.
Citation
Qiang Ren, Luis E. Tobon, and Qing Huo Liu, "A New 2D Non-Spurious Discontinuous Galerkin Finite Element Time Domain (DG-FETD) Method for Maxwell's Equations," Progress In Electromagnetics Research, Vol. 143, 385-404, 2013.
doi:10.2528/PIER13100901
References

1. Jin, J., The Finite Element Method in Electromagnetics, Wiley, 2007.

2. Monk, P., Finite Element Method for Maxwells Equations, Oxford, 2003.
doi:10.1093/acprof:oso/9780198508885.001.0001

3. Silvester, P. and R. Ferrari, "Finite Elements for Electrical Engineers," Cambridge University Press, 1996.

4. Andersen, L. and J. Volakis, "Development and application of a novel class of hierarchical tangential vector finite elements for electromagnetics," IEEE. Trans. Antennas Propagat., Vol. 47, No. 1, 112-120, 1999.
doi:10.1109/8.753001

5. Volakis, J., T. Ozdemir, and J. Gong, "Hybrid finite-element methodologies for antennas and scattering," IEEE. Trans. Antennas Propagat., Vol. 45, No. 3, 493-507, 1997.
doi:10.1109/8.558664

6. Tonti, E., "Finite formulation of the electromagnetic fiel," Progress In Electromagnetics Research, Vol. 32, 1-44, 2001.
doi:10.2528/PIER00080101

7. Polycarpou, A., P. Tirkas, and C. Balanis, "The finite-element method for modeling circuits and interconnects for electronic packaging," IEEE Trans. Microw. Theory Techn., Vol. 45, No. 10, 1868-1874, 1997.
doi:10.1109/22.641784

8. Lee, J., R. Lee, and A. Cangellaris, "Time-domain finite-element methods," IEEE. Trans. Antennas Propagat., Vol. 45, No. 3, 430-442, 1997.
doi:10.1109/8.558658

9. Jiao, D. and J. Jin, "A general approach for the stability analysis of the time-domain finite-element method for electromagnetic simulations," IEEE. Trans. Antennas Propagat., Vol. 50, No. 11, 1624-1632, 2002.
doi:10.1109/TAP.2002.803965

10. Petersson, L. and J. Jin, "A three-dimensional time-domain finite-element formulation for periodic structures," IEEE. Trans. Antennas Propagat., Vol. 54, No. 1, 12-19, 2006.
doi:10.1109/TAP.2005.861547

11. Vaseghi, B., N. Takorabet, and F. Meibody-Tabar, "Transient finite element analysis of induction machines with stator winding turn fault," Progress In Electromagnetics Research, Vol. 95, 1-18, 2009.
doi:10.2528/PIER09052004

12. Faghihi, F. and H. Heydari, "A combination of time domain finite element-boundary integral and with time domain physical optics for calculation of electromagnetic scattering of 3-D structures ," Progress In Electromagnetics Research, Vol. 79, 463-474, 2008.
doi:10.2528/PIER07110206

13. Mur, G., "The finite-element modeling of three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media," IEEE Trans. Magn., Vol. 28, No. 2, 1130-1133, 1992.
doi:10.1109/20.123883

14. Gedney, S. and U. Navsariwala, "An unconditionally stable finite element time-domain solution of the vector wave equation," IEEE Microw. Guided Wave Lett., Vol. 5, No. 10, 332-334, 1995.
doi:10.1109/75.465046

15. Tsai, H., Y. Wang, and T. Itoh, "An unconditionally stable extended (USE) finite-element time-domain solution of active nonlinear microwave circuits using perfectly matched layers," IEEE Trans. Microw. Theory Techn., Vol. 50, No. 10, 2226-2232, 2002.
doi:10.1109/TMTT.2002.803442

16. Jiao, D., J. Jin, E. Michielssen, and D. Riley, "Time-domain finiteelement simulation of three-dimensional scattering and radiation problems using perfectly matched layers ," IEEE. Trans. Antennas Propagat., Vol. 51, No. 2, 296-305, 2003.
doi:10.1109/TAP.2003.809096

17. Cangellaris, A. and Point-matched time, "Point-matched time domain finite element methods for electromagnetic radiation and scattering," IEEE. Trans. Antennas Propagat., Vol. 35, No. 10, 1160-1173, 1987.
doi:10.1109/TAP.1987.1143981

18. Wong, M., O. Picon, and V. Fouad Hanna, "A finite element method based on whitney forms to solve Maxwell equations in the time domain," IEEE Trans. Magn., Vol. 31, No. 3, 1618-1621, 1995.
doi:10.1109/20.376343

19. Feliziani, M. and F. Maradei, "An explicit-implicit solution scheme to analyze fast transients by finite elements," IEEE Trans. Magn., Vol. 33, No. 2, 1452-1455, 1997.
doi:10.1109/20.582533

20. Donderici, B. and F. Teixeira, "Mixed finite-element time-domain method for transient Maxwell equations in doubly dispersive media," IEEE Trans. Microw. Theory Techn., Vol. 56, No. 1, 113-120, 2008.
doi:10.1109/TMTT.2007.912217

21. Donderici, B. and F. Teixeira, "Conformal perfectly matched layer for the mixed finite element time-domain method," IEEE. Trans. Antennas Propagat., Vol. 56, No. 4, 1017-1026, 2008.
doi:10.1109/TAP.2008.919215

22. Yioultsis, T., N. Kantartzis, C. Antonopoulos, and T. Tsiboukis, "A fully explicit whitney element-time domain scheme with higher order vector ¯nite elements for three-dimensional high frequency problems ," IEEE Trans. Magn., Vol. 34, No. 5, 3288-3291, 1998.
doi:10.1109/20.717772

23. Guillouard, K., M. Wong, V. Fouad Hanna, and J. Citerne, "A new global time-domain electromagnetic simulator of microwave circuits including lumped elements based on finite-element method," IEEE Trans. Microw. Theory Techn., Vol. 47, No. 10, 2045-2049, 1999.
doi:10.1109/22.795085

24. Sekine, T. and H. Asai, "Mixed finite element time domain method based on iterative leapfrog scheme for fast simulations of electromagnetic problems," IEEE International Symposium on Electromagnetic Compatibility (EMC), 2011, 596-601, 2011.
doi:10.1109/ISEMC.2011.6038381

25. Cohen, G. and M. Durufle, "Non spurious spectral-like element methods for Maxwell's equations," J. Comput. Math., Vol. 25, 282-300, 2007.

26. Winkler, J. R. and J. B. Davies, "Elimination of spurious modes in finite element analysis," J. Computat. Phys., Vol. 56, 1-14, 1984.
doi:10.1016/0021-9991(84)90079-2

27. Tobon, L., J. Chen, and Q. H. Liu, "Spurious solutions in mixed finite element method for Maxwell's equations: Dispersion analysis and new basis functions," J. Computat. Phys., Vol. 230, No. 19, 7300-7310, 2011.
doi:10.1016/j.jcp.2011.05.035

28. Chen, J., L. Tobon, M. Chai, J. Mix, and Q. H. Liu, "Effcient implicit-explicit time stepping scheme with domain decomposition for multiscale modeling of layered structures ," IEEE Trans. Compon. Packag. Manuf. Technol., Vol. 1, No. 9, 1438-1446, 2011.
doi:10.1109/TCPMT.2011.2162726

29. Chen, J. and Q. H. Liu, "A non-spurious vector spectral element method for Maxwell's equations," Progress In Electromagnetics Research, Vol. 96, 205-215, 2009.
doi:10.2528/PIER09082705

30. Cangellaris, A. and H. Wu, "Domain decomposition and multi-scale finite elements for electromagnetic analysis of integrated electronic systems ," IEEE International Symposium on Electromagnetic Compatibility (EMC), 2005, Vol. 3, 817-822, 2005.

31. Gedney, S., T. Kramer, C. Luo, J. Roden, R. Crawford, B. Guernsey, J. Beggs, and J. Miller, "The discontinuous Galerkin finite element time domain method (DGFETD)," IEEE International Symposium on Electromagnetic Compatibility (EMC), 2008 , 1-4, 2008.
doi:10.1109/ISEMC.2008.4652146

32. Lu, T., W. Cai, and P. Zhang, "Discontinuous Galerkin time domain method for gpr simulation in dispersive media," IEEE Trans. Seosci. Remote Sens., Vol. 43, No. 1, 72-80, 2005.
doi:10.1109/TGRS.2004.838350

33. Gan, H. and D. Jiao, "A time-domain layered finite element reduction recovery (LAFE-RR) method for high-frequency VLSI design," IEEE. Trans. Antennas Propagat., Vol. 55, No. 12, 3620-3629, 2007.
doi:10.1109/TAP.2007.910473

34. Canouet, N., L. Fezoui, and S. Piperno, "Discontinuous Galerkin time-domain solution of Maxwell's equations on locally-refined nonconforming cartesian grids ," COMPEL: Int. J. for Computation and Maths. in Electrical and Electronic Eng., Vol. 24, No. 4, 1381-1401, 2005.
doi:10.1108/03321640510615670

35. Shi, Y. and C.-H. Liang, "Simulations of the left-handed medium using discontinuous Galerkin method based on the hybrid domains ," Progress In Electromagnetics Research, Vol. 63, 171-191, 2006.
doi:10.2528/PIER06050803

36. Nedelec, J., "A new family of mixed finite elements in R3," Numerische Mathematik, Vol. 50, No. 1, 57-81, 1986.
doi:10.1007/BF01389668

37. Nedelec, J., "Mixed finite elements in R3," Numerische Mathematik, Vol. 35, No. 3, 315-341, 1980.
doi:10.1007/BF01396415

38. Peterson, A., S. Ray, and R. Mittra, , Computational Methods for Electromagnetics, Vol. 24, IEEE Press, 1998.

39. Fan, G.-X. and Q. H. Liu, "A strongly well-posed PML in lossy media," IEEE Antennas Wireless Propagat. Lett., Vol. 2, No. 7, 97-100, 2003.

40. Liu, Q. H., "The PSTD algorithm: A time-domain method requiring only two cells per wavelength," Microwave and Optical Technology Letters, Vol. 15, 158-165, 1997.
doi:10.1002/(SICI)1098-2760(19970620)15:3<158::AID-MOP11>3.0.CO;2-3