Advertisement

Introduction

  • Thomas Rylander
  • Pär Ingelström
  • Anders Bondeson
Chapter
Part of the Texts in Applied Mathematics book series (TAM)

Abstract

Our modern society relies on electromagnetic devices and systems: television, radio, internet, microwave ovens, mobile telephones, satellite communication systems, radar systems, electrical motors, electrical generators, computers, microwave filters, lasers, industrial heating devices, medical imaging systems, electrical power networks, transformers and many more. Each of these examples is used in a broad range of situations. Radar, for example, is employed for fire-control, weather detection, airport traffic-control, missile tracking, missile guidance, speed control/enforcement, and traffic safety. Undoubtedly, electromagnetic phenomena have a profound impact on contemporary society.

Keywords

Absorb Boundary Condition Perfect Electric Conductor Electromagnetic Phenomenon Electrical Power Network Electric Power Engineering 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    T Abboud, J C Nédélec, and J Volakis. Stable solution of the retarded potential equations. 17th Annual Review of Progress in Applied Computational Electromagnetics, Monterey, CA, pages 146–151, 2001.Google Scholar
  2. 2.
    M Abramowitz and I A Stegun. Handbook of Mathematical Functions. National Bureau of Standards, 1965.Google Scholar
  3. 3.
    F Alimenti, P Mezzanotte, L Roselli, and R Sorrentino. A revised formulation of model absorbing and matched modal source boundary conditions for the efficient FDTD analysis of waveguide structures. IEEE Trans. Microwave Theory Tech., 48(1):50–59, January 2000.CrossRefGoogle Scholar
  4. 4.
    O Axelsson. Iterative Solution Methods. New York, NY: Cambridge University Press, 1994.CrossRefMATHGoogle Scholar
  5. 5.
    C A Balanis. Advanced Engineering Electromagnetics. New York, NY: John Wiley & Sons, 1989.Google Scholar
  6. 6.
    S Balay, W Gropp, L Curfman McInnes, and B Smith. The portable, extensible toolkit for scientific computation. http://www-unix.mcs.anl.gov/petsc/petsc-2/, 2005.
  7. 7.
    R Barret, M Berry, T F Chan, J Demmel, J Donato, J Dongarra, V Eijkhout, R Pozo, C Romine, and H Van der Vorst. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia, PA, 1994. available at: ftp://ftp.netlib.org/templates/templates.ps.Google Scholar
  8. 8.
    R Beck and R Hiptmair. Multilevel solution of the time-harmonic Maxwell’s equations based on edge elements. Int. J. Numer. Meth. Engng., 45(7):901–920, 1999.CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    J P Bérenger. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys., 114(2):185–200, October 1994.Google Scholar
  10. 10.
    J Bey. Tetrahedral grid refinement. Computing, 55(4):355–378, 1995.CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    M J Bluck and S P Walker. Time-domain BIE analysis of large three-dimensional electromagnetic scattering problems. IEEE Trans. Antennas Propagat., 45(5):894–901, May 1997.Google Scholar
  12. 12.
    Alain Bossavit. Computational Electromagnetism. Boston, MA: Academic Press, 1998.MATHGoogle Scholar
  13. 13.
    M M Botha and J M Jin. On the variational formulation of hybrid finite element–boundary integral techniques for electromagnetic analysis. IEEE Trans. Antennas Propagat., 52(11):3037–3047, November 2004.Google Scholar
  14. 14.
    A C Cangellaris and D B Wright. Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena. IEEE Trans. Antennas Propagat., 39(10):1518–1525, October 1991.Google Scholar
  15. 15.
    F X Canning. Improved impedance matrix localization method. IEEE Trans. Antennas Propagat., 41(5):659–667, May 1993.Google Scholar
  16. 16.
    F X Canning and K Rogovin. Fast direct solution of standard moment-method matrices. IEEE Antennas Propagat. Mag., 40(3):15–26, June 1998.Google Scholar
  17. 17.
    M Celuch-Marcysiak and W K Gwarek. Generalized TLM algorithms with controlled stability margin and their equivalence with finite-difference formulations for modified grids. IEEE Trans. Microwave Theory Tech., 43(9):2081–2089, September 1995.Google Scholar
  18. 18.
    Z Chen, M M Ney, and W J R Hoefer. A new finite-difference time-domain formulation and its equivalence with the TLM symmetrical condensed node. IEEE Trans. Microwave Theory Tech., 39(12):2160–2169, December 1991.Google Scholar
  19. 19.
    D K Cheng. Fundamentals of Engineering Electromagnetics. Reading, MA: Addison-Wesley, 1993.Google Scholar
  20. 20.
    W C Chew, J M Jin, E Michielssen, and J Song. Fast and Efficient Algorithms in Computational Electromagnetics. Norwood, MA: Artech House, 2001.Google Scholar
  21. 21.
    R Coifman, V Rokhlin, and S Wandzura. The fast multipole method for the wave equation: A pedestrian prescription. IEEE Antennas Propagat. Mag., 35(3):7–12, June 1993.CrossRefGoogle Scholar
  22. 22.
    D B Davidson. Computational Electromagnetics for RF and Microwave Engineering. Cambridge: Cambridge University Press, second edition, 2011.Google Scholar
  23. 23.
  24. 24.
    J W Demmel, J R Gilbert, and X S Li. SuperLU. http://crd.lbl.gov/~xiaoye/SuperLU/, 2005.
  25. 25.
    S J Dodson, S P Walker, and M J Bluck. Costs and cost scaling in time-domain integral-equation analysis of electromagnetic scattering. IEEE Antennas Propagat. Mag., 40(4):12–21, August 1998.Google Scholar
  26. 26.
    R Dyczij-Edlinger and O Biro. A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements. IEEE Trans. Microwave Theory Tech., 44(1):15–23, 1996.CrossRefGoogle Scholar
  27. 27.
    R Dyczij-Edlinger, G Peng, and J F Lee. A fast vector-potential method using tangentially continuous vector finite elements. IEEE Trans. Microwave Theory Tech., 46(6):863–868, 1998.Google Scholar
  28. 28.
    K Eriksson, D Estep, P Hansbo, and C Johnson. Computational Differential Equations. New York, NY: Cambridge University Press, 1996.MATHGoogle Scholar
  29. 29.
    R Garg. Analytical and Computational Methods in Electromagnetics. Norwood, MA: Artech House, 2008.MATHGoogle Scholar
  30. 30.
    W L Golik. Wavelet packets for fast solution of electromagnetic integral equations. IEEE Trans. Antennas Propagat., 46(5):618–624, May 1998.Google Scholar
  31. 31.
    R D Graglia. On the numerical integration of the linear shape functions times the 3-D Green’s function or its gradient on a plane triangle. IEEE Trans. Antennas Propagat., 41(10):1448–1455, October 1993.Google Scholar
  32. 32.
    D J Griffiths. Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice-Hall, third edition, 1999.Google Scholar
  33. 33.
    W Hackbusch. Multi-Grid Methods and Application. Berlin: Springer-Verlag, 1985.CrossRefGoogle Scholar
  34. 34.
    W Hackbush. Iterative Solution of Large Sparse Linear Systems of Equations. New York, NY: Springer-Verlag, 1994.CrossRefGoogle Scholar
  35. 35.
    V Hill, O Farle, and R Dyczij-Edlinger. A stabilized multilevel vector finite-element solver for time-harmonic electromagnetic waves. IEEE Trans. Magn., 39(3):1203–1206, 2003.CrossRefGoogle Scholar
  36. 36.
    R Hiptmair. Multigrid method for Maxwell’s equations. SIAM J. Numer. Anal., 36(1):204–225, 1998.CrossRefMATHMathSciNetGoogle Scholar
  37. 37.
    W J R Hoefer. The transmission-line method – theory and applications. IEEE Trans. Microwave Theory Tech., 33(10):882–893, October 1985.Google Scholar
  38. 38.
    T J R Hughes. The finite element method: linear static and dynamic finite element analysis. Englewood Cliffs, NJ: Prentice-Hall, 1987.MATHGoogle Scholar
  39. 39.
    P Ingelström. Higher Order Finite Elements and Adaptivity in Computational Electromagnetics. PhD thesis, Chalmers University of Technology, Göteborg, Sweden, 2004.Google Scholar
  40. 40.
    J M Jin. The Finite Element Method in Electromagnetics. New York, NY: John Wiley & Sons, 1993.MATHGoogle Scholar
  41. 41.
    J M Jin. The Finite Element Method in Electromagnetics. New York, NY: John Wiley & Sons, second edition, 2002.Google Scholar
  42. 42.
    J M Jin. Theory and Computation of Electromagnetic Fields. New York, NY: John Wiley & Sons, 2010.CrossRefGoogle Scholar
  43. 43.
    P B Johns. A symmetrical condensed node for the TLM method. IEEE Trans. Microwave Theory Tech., 35(4):370–377, April 1987.Google Scholar
  44. 44.
  45. 45.
    P S Kildal, S Rengarajan, and A Moldsvor. Analysis of nearly cylindrical antennas and scattering problems using a spectrum of two-dimensional solutions. IEEE Trans. Antennas Propagat., 44(8):1183–1192, August 1996.Google Scholar
  46. 46.
    Y Q Liu, A Bondeson, R Bergström, C Johnson, M G Larson, and K Samuelsson. Eddy-current computations using adaptive grids and edge elements. IEEE Trans. Magn., 38(2):449–452, March 2002.Google Scholar
  47. 47.
    N K Madsen and R W Ziolkowski. A three-dimensional modified finite volume technique for maxwell’s equations. Electromagnetics, 10(1-2):147–161, January-June 1990.Google Scholar
  48. 48.
    P Monk. Finite Element Methods for Maxwell’s Equations. Oxford: Clarendon Press, 2003.CrossRefMATHGoogle Scholar
  49. 49.
    P B Monk. A comparison of three mixed methods for the time dependent Maxwell equations. SIAM Journal on Scientific and Statistical Computing, 13(5):1097–1122, September 1992.Google Scholar
  50. 50.
    A Monorchio and R Mittra. A hybrid finite-element finite-difference time-domain (FE/FDTD) technique for solving complex electromagnetic problems. IEEE Microw. Guided Wave Lett., 8(2):93–95, February 1998.CrossRefGoogle Scholar
  51. 51.
    J C Nédélec. Mixed finite elements in R3. Numer. Math., 35(3):315–341, 1980.Google Scholar
  52. 52.
    N M Newmark. A method of computation for structural dynamics. J. Eng. Mech. Div., Proc. Am. Soc. Civil Eng., 85(EM 3):67–94, July 1959.Google Scholar
  53. 53.
    S Owen. Meshing Research Corner. http://www.andrew.cmu.edu/user/sowen/mesh.html, 2005.
  54. 54.
    A F Peterson, S L Ray, and R Mittra. Computational Methods for Electromagnetics. New York, NY: IEEE Press, 1997.CrossRefGoogle Scholar
  55. 55.
    P G Petropoulos, L Zhao, and A C Cangellaris. A reflectionless sponge layer absorbing boundary condition for the solution of Maxwell’s equations with high-order staggered finite difference schemes. J. Comput. Phys., 139(1):184–208, January 1998.Google Scholar
  56. 56.
    A J Poggio and E K Miller. Integral equation solutions of three-dimensional scattering problems. Computer Techniques for Electromagnetics, Oxford: Pergamon:159–264, 1973.Google Scholar
  57. 57.
    S M Rao and D R Wilton. Transient scattering by conducting surfaces of arbitrary shape. IEEE Trans. Antennas Propagat., 39(1):56–61, January 1991.Google Scholar
  58. 58.
    S M Rao, D R Wilton, and A W Glisson. Electromagnetic scattering by surfaces of arbitrary shape. IEEE Trans. Antennas Propagat., AP-30(3):409–418, May 1982.Google Scholar
  59. 59.
    S Reitzinger and M Kaltenbacher. Algebraic multigrid methods for magnetostatic field problems. IEEE Trans. Magn., 38(2):477–480, 2002.CrossRefGoogle Scholar
  60. 60.
    D J Riley and C D Turner. VOLMAX: A solid-model-based, transient volumetric Maxwell solver using hybrid grids. IEEE Antennas Propagat. Mag., 39(1):20–33, February 1997.Google Scholar
  61. 61.
    V Rokhlin. Rapid solution of integral equations of classical potential theory. J. Comput. Phys., 60(2):187–207, 1985.CrossRefMATHMathSciNetGoogle Scholar
  62. 62.
    V Rokhlin. Rapid solution of integral equations of scattering theory in two dimensions. J. Comput. Phys., 86(2):414–439, 1990.CrossRefMATHMathSciNetGoogle Scholar
  63. 63.
    T Rylander and A Bondeson. Stability of explicit-implicit hybrid time-stepping schemes for Maxwell’s equations. J. Comput. Phys., 179(2):426–438, July 2002.CrossRefMATHGoogle Scholar
  64. 64.
    T Rylander and J M Jin. Perfectly matched layer for the time domain finite element method. J. of Comput. Phys., 200(1):238–250, October 2004.Google Scholar
  65. 65.
    T Rylander, T McKelvey, and M Viberg. Estimation of resonant frequencies and quality factors from time domain computations. J. of Comput. Phys., 192(2):523–545, December 2003.CrossRefMATHGoogle Scholar
  66. 66.
    B P Rynne. Instabilities in time marching methods for scattering problems. Electromagnetics, 6(2):129–144, 1986.Google Scholar
  67. 67.
    Y Saad. Iterative methods for sparse linear systems. Boston, MA: PWS Publishing, 1996.MATHGoogle Scholar
  68. 68.
    M N O Sadiku. Numerical Techniques in Electromagnetics with MATLAB. Boca Raton, FL: CRC Press, third edition, 2009.Google Scholar
  69. 69.
    M Salazar-Palma, T K Sarkar, L E Garcia-Castillo, T Roy, and A Djordjevic. Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling. Norwood, MA: Artech House, 1998.MATHGoogle Scholar
  70. 70.
    M Schinnerl, J Schöberl, and M Kaltenbacher. Nested multigrid methods for the fast numerical computation of 3D magnetic fields. IEEE Trans. Magn., 36(4):1557–1560, 2000.CrossRefGoogle Scholar
  71. 71.
    R Schuhmann and T Weiland. Stability of the FDTD algorithm on nonorthogonal grids related to the spatial interpolation scheme. IEEE Trans. Magn., 34(5):2751–2754, September 1998.CrossRefGoogle Scholar
  72. 72.
    X Q Sheng and W Song. Essentials of Computational Electromagnetics. Singapore: John Wiley & Sons, 2012.CrossRefGoogle Scholar
  73. 73.
    J R Shewchuk. Trianlge – a two-dimensional quality mesh generator and delaunay triangulator. http://www.cs.cmu.edu/~quake/triangle.html.
  74. 74.
    J R Shewchuk. Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. Lecture Notes in Computer Science, 1148:203–222, May 1996.Google Scholar
  75. 75.
    P P Silvester and R L Ferrari. Finite Elements for Electrical Engineers. New York, NY: Cambridge University Press, second edition, 1990.Google Scholar
  76. 76.
    P D Smith. Instabilities in time marching methods for scattering: cause and rectification. Electromagnetics, 10(4):439–451, October–December 1990.Google Scholar
  77. 77.
    J M Song and W C Chew. The fast Illinois solver code: requirements and scaling properties. IEEE Comput. Sci. Eng., 5(3):19–23, July–September 1998.Google Scholar
  78. 78.
    J M Song, C C Lu, and W C Chew. Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects. IEEE Trans. Antennas Propagat., 45(10):1488–1493, October 1997.Google Scholar
  79. 79.
    J M Song, C C Lu, W C Chew, and S W Lee. Fast Illinois solver code (FISC). IEEE Antennas Propagat. Mag., 40(3):27–34, June 1998.Google Scholar
  80. 80.
    A Taflove. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech House, 1995.MATHGoogle Scholar
  81. 81.
    A Taflove, editor. Advances in Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech House, 1998.MATHGoogle Scholar
  82. 82.
    A Taflove and S C Hagness. Computational Electrodynamics: The Finite-Difference Time-Domain Method. Norwood, MA: Artech House, second edition, 2000.Google Scholar
  83. 83.
    P Thoma and T Weiland. Numerical stability of finite difference time domain methods. IEEE Trans. Magn., 34(5):2740–2743, September 1998.CrossRefGoogle Scholar
  84. 84.
    S Toledo, D Chen, and V Rotkin. TAUCS, A Library of Sparse Linear Solvers. http://www.tau.ac.il/~stoledo/taucs/, 2005.
  85. 85.
    D A Vechinski and S M Rao. A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape. IEEE Trans. Antennas Propagat., 40(6):661–665, June 1992.Google Scholar
  86. 86.
    R L Wagner and W C Chew. A study of wavelets for the solution of electromagnetic integral equations. IEEE Trans. Antennas Propagat., 43(8):802–810, August 1995.Google Scholar
  87. 87.
    J J H Wang. Generalized Moment Methods in Electromagnetics. New York, NY: John Wiley & Sons, 1991.Google Scholar
  88. 88.
    K F Warnick. NUMERICAL METHODS FOR ENGINEERING - An Introduction Using MATLAB and Computational Electromagnetics Examples. Raleigh, NC: SciTech Publishing, 2011.Google Scholar
  89. 89.
    J P Webb. Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements. IEEE. Trans. Antennas Propagat., 47(8):1244–1253, 1999.Google Scholar
  90. 90.
    T Weiland. Time domain electromagnetic field computation with finite difference methods. Int. J. Numer. Model. El., 9(4):295–319, July-August 1996.Google Scholar
  91. 91.
    P Wesseling. An Introduction to Multigrid Methods. Chichester: John Wiley & Sons, 1992.MATHGoogle Scholar
  92. 92.
    R B Wu and T Itoh. Hybrid finite-difference time-domain modeling of curved surfaces using tetrahedral edge elements. IEEE Trans. Antennas Propagat., 45(8):1302–1309, August 1997.Google Scholar
  93. 93.
    K S Yee. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propagat., AP-14(3):302–307, May 1966.Google Scholar
  94. 94.
    K S Yee and J S Chen. The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell’s equations. IEEE Trans. Antennas Propagat., 45(3):354–363, March 1997.Google Scholar
  95. 95.
    K S Yee, J S Chen, and A H Chang. Numerical experiments on PEC boundary condition and late time growth involving the FDTD/FDTD and FDTD/FVTD hybrid. IEEE Antennas Propagat. Soc. Int. Symp., 1:624–627, 1995.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Thomas Rylander
    • 1
  • Pär Ingelström
    • 2
  • Anders Bondeson
  1. 1.Department of Signals and SystemsChalmers University of TechnologyGöteborgSweden
  2. 2.Department of ElectromagneticsChalmers University of TechnologyGöteborgSweden

Personalised recommendations