Search search
submit Submit
Publication Date
to
Vol. 149
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
2014-08-23
Surface and Volume Integral Equation Methods for Time-Harmonic Solutions of Maxwell's Equations (Invited Paper)
By
Pasi Yla-Oijala,

    Dr. Pasi Yla-Oijala

    Department of Radio Science and Engineering

    Aalto University

    Finland

    Homepage

Johannes Markkanen,

    Dr. Johannes Markkanen

    Department of Physics

    University of Helsinki

    Finland

    Homepage

Seppo Jarvenpaa,

    Dr. Seppo Jarvenpaa

    Aalto Univ

    Finland

    Homepage

Sami P. Kiminki

    Dr. Sami P. Kiminki

    Department of Radio Science and Engineering

    Aalto University

    Finland

    Homepage

Progress In Electromagnetics Research, Vol. 149, 15-44, 2014
doi:10.2528/PIER14070105
Abstract
During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell's has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume integral equation methods for finding time-harmonic solutions of Maxwell's equations. First a review of classical integral equation representations and formulations is given. Thereafter we briefly overview the mathematical background of integral operators and equations and their discretization with the method of moments. The main focus is on advanced techniques that would enable accurate, stable, and scalable solutions on a wide range of material parameters, frequencies and applications. Finally, future perspectives of the integral equation methods for solving Maxwell's equations are discussed.
Citation
Pasi Yla-Oijala, Johannes Markkanen, Seppo Jarvenpaa, and Sami P. Kiminki, "Surface and Volume Integral Equation Methods for Time-Harmonic Solutions of Maxwell's Equations (Invited Paper)," Progress In Electromagnetics Research, Vol. 149, 15-44, 2014.
doi:10.2528/PIER14070105
References

1. Williams, L. and S. Rousselle, "EM at the core of complex microwave system design," IEEE Microwave Magazine, 97-104, Dec. 2008.

2. Weiland, T., M. Timm, and I. Munteanu, "A practical guide to 3-D simulation," IEEE Microwave Magazine, 62-75, Dec. 2008.

3. Maxwell, J. C., A Treatise of Electricity and Magnetism, Clarendon Press, Oxford, 1873.

4. Heavyside, O., "On electromagnetic waves, especially in relation to the vorticity of the impressed forces, and the forced vibration of electromagnetic systems," Philos. Mag., Vol. 25, 130-156, 1888.

5. Chew, W. C., M. S. Tong, and B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, Morgan & Claypool Publishers, 2009.

6. Chew, W. C., J.-M. Jin, E. Michielssen, and J. Song, Fast and Efficient Algorithms in Computational Electromagnetics, Artech House, Boston, 2001.

7. Volakis, J. L., A. Chatterjee, and L. C. Kempel, Finite Element Method for Electromagnetics, IEEE Press, New York, 1998.

8. Jin, J., The Finite Element Method in Electromagnetics, John Wiley & Sons, New York, 2002.

9. Zhu, Y. and A. C. Cangellaris, Multigrid Finite Element Methods for Electromagnetic Field Modeling, IEEE Press, John Wiley & Sons, New Jersey , 2006.

10. Yee, K. S., "Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media," IEEE Trans. Antennas Propag., Vol. 14, No. 3, 302-307, 1966.

11. Taflove, A., Computational Electrodynamics, The Finite-difference Time-domain Method, Artech House, Boston, 1995.

12. Gedney, S. D., Introduction to the FDTD Method for Electromagnetics, Morgan & Claypool, 2011.

13. Kolundzija, B. M. and A. R. Djordjevic, Electromagnetic Modeling of Composite Metallic and Dielectric Structures, Artech House, Boston, 2002.

14. Volakis, J. L. and K. Sertel, Integral Equation Methods for Electromagnetics, Scitech Publishing, Inc., 2012.

15. Chew, W. C., Wave and Fields in Inhomogeneous Media, IEEE Press, New York, 1990.

16. Stratton, J. A. and L. J. Chu, "Diffraction theory of electromagnetic waves," Physical Review, Vol. 56, 99-107, 1939.

17. Mei, K. K. and J. G. van Bladel, "Scattering by perfectly conducting rectangular cylinders," IEEE Trans. Antennas Propag., Vol. 11, No. 2, 185-192, Mar. 1963.

18. Andreasen, M. G., "Scattering from parallel metallic cylinders with arbitrary cross section," IEEE Trans. Antennas Propag., Vol. 12, No. 6, 746-754, Nov. 1964.

19. Richmond, J. H., "Scattering by a dielectric cylinder of arbitrary cross-section shape," IEEE Trans. Antennas Propag., Vol. 13, No. 3, 338-341, May 1965.

20. Mei, K. K., "On the integral equations for thin wire antennas," IEEE Trans. Antennas Propag., Vol. 13, No. 3, 374-378, May 1965.

21. Richmond, J. H., "Scattering by an arbitrary array of parallel wires," IEEE Trans. Microw. Theory Techn., Vol. 13, No. 4, 408-412, May 1965.

22. Wu, T. K. and L. L. Tsai, "Scattering from arbitrarily-shaped lossy dielectric bodies of revolution," Radio Science, Vol. 12, No. 5, 709-718, 1977.

23. Mautz, J. R. and R. F. Harrington, "H-field, E-field and combined-field solutions for conducting bodies of revolution," Arch. Elektron. ¨ Ubertragungstechn. (Electron. Commun.), Vol. 32, 157-164, 1978.

24. Mautz, J. R. and R. F. Harrington, "Electromagnetic scattering from a homogeneous material body of revolution," Arch. Elektron. ¨ Ubertragungstechn. (Electron. Commun.), Vol. 33, 71-80, 1979.

25. Rao, S. M., D. R. Wilton, and A. W. Glisson, "Electromagnetic scattering by surfaces of arbitrary shape," IEEE Trans. Antennas Propag., Vol. 30, No. 3, 409-418, 1982.

26. Umashankar, K., A. Taflove, and S. A. Rao, "Electromagnetic scattering by arbitrary shaped three-dimensional homogeneous lossy dielectric objects," IEEE Trans. Antennas Propag., Vol. 34, No. 6, 758-766, 1986.

27. Medgyesi-Mitschang, L. N., J.M. Putnam, and M. B. Gedera, "Generalized method of moments for three-dimensional penetrable scatterers," J. Opt. Soc. America, A, Vol. 11, 1383-1398, Apr. 1994.

28. Glisson, A. W., "Electromagnetic scattering with impedance boundary conditions," Radio Science, Vol. 27, No. 6, 935-943, 1992.

29. Chew, W. C., H. Y. Chao, T. J. Cui, C. C. Lu, S. Ohnuki, Y. C. Pan, J.M. Song, S. Velamparambil, and J. S. Zhao, "Fast integral equation solvers in computational electromagnetics," Eng. Anal. Boundary Elem., Vol. 27, 803-823, 2003.

30. Sarkar, T. K., E. Arvas, and S. M. Rao, "Application of FFT and the conjugate gradient method for the solution of electromagnetic radiation from electrically large and small conducting bodies," IEEE Trans. Antennas Propag., Vol. 34, No. 5, 635-640, 1986.

31. Peters, T. J. and J. L. Volakis, "Application of a conjugate gradient FFT method to scattering from thin planar material plates," IEEE Trans. Antennas Propag., Vol. 36, No. 4, 518-526, 1988.

32. Zwamborn, A. P. M. and P. M. van den Berg, "Computation of electromagnetic fields inside strongly inhomogeneous objects by the weak-conjugate-gradient fast-Fourier-transform method," J. Opt. Soc. Am. A,, Vol. 11, 1414-1420, 1994.

33. Gan, H. and W. C. Chew, "A discrete BCG-FFT algorithm for solving 3D inhomogeneous scattering problems," Journal of Electromagnetic Waves and Applications, Vol. 9, No. 10, 1339-1357, 1995.

34. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "AIM: Adaptive integral method for solving large-scale electromagnetic scattering and radiation problems," Radio Science, Vol. 31, No. 5, 1225-1251, Sep.-Oct. 1996.

35. Phillips, J. R. and J. K. White, "A precorrected-FFT method for electrostatic analysis of complicated 3-D structures," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems, Vol. 16, No. 10, 1059-1072, 1997.

36. Rokhlin, V., "Rapid solution of integral equations of scattering theory in two dimensions," J. Comput. Physics, Vol. 86, No. 2, 414-439, 1990.

37. Song, J. M. and W. C. Chew, "Multilevel fast-multipole algorithm for solving combined field integral equations of electromagnetic scattering," Microw. Opt. Techn. Lett., Vol. 10, No. 1, 14-19, 1995.

38. Song, J. M., C. C. Lu, and W. C. Chew, "Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects," IEEE Trans. Antennas Propag., Vol. 45, No. 10, 1488-1493, 1997.

39. Sheng, X.-Q., J.-M. Jin, J. Song, W. C. Chew, and C.-C. Lu, "Solution of combined-field integral equation using multilevel fast multipole algorithm for scattering by homogeneous bodies," IEEE Trans. Antennas Propag., Vol. 46, No. 11, 1718-1726, 1998.

40. Pan, X.-M. and X.-Q. Sh, "A sophisticated parallel MLFMA for scattering by extremely large targets," IEEE Antennas Propag. Mag., Vol. 50, No. 3, 129-138, 2008.

41. Ergul , O. and L. Gure, "Rigorous solutions of electromagnetics problems involving hundreds of millions of unknowns," IEEE Antennas Propag. Mag., Vol. 53, No. 1, 18-27, 2011.

42. Zhao, J.-S. and W. C. Chew, "Integral equation solution of Maxwell’s equations from zero frequency to microwave frequencies," IEEE Trans. Antennas Propag., Vol. 48, No. 10, 1635-1645, 2000.

43. Adam, R. J., "Physical and analytical properties of a stabilized electric field integral equation," IEEE Trans. Antennas Propag., Vol. 52, No. 2, 362-372, 2004.

44. Vipiana, F., P. Pirinoli, and G. Vecchi, "A multiresolution method of moments for triangular meshes," IEEE Trans. Antennas Propag., Vol. 53, No. 7, 2247-2258, 2005.

45. Andriulli, F. P., K. Cools, H. Bagci, F. Olyslager, A. Buffa, S. Christiansen, and E. Michielssen, "A multiplicative Calderon preconditioner for the electric field integral equation," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2398-2412, 2008.

46. Qian, Z. G. and W. C. Chew, "An augmented electric field integral equation for high-speed interconnect analysis," Microw. Opt. Techn. Lett., Vol. 50, No. 10, 2658-2662, 2008.

47. Andriulli, F. P., K. Cools, I. Bogaert, and E. Michielssen, "On a well-conditioned electric-field integral operator for multiple connected geometries," IEEE Trans. Antennas Propag., Vol. 61, No. 4(2), 2077-2087, 2013.

48. Yla-Oijala, P., M. Taskinen, and S. Jarvenpaa, "Surface integral equation formulations for solving electromagnetic scattering problems with iterative methods," Radio Science, Vol. 40, No. 6, RS6002, 2005.

49. Taskinen, M. and P. Yla-Oijala, "Current and charge integral equation formulation," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 58-67, 2006.

50. Epstein, C. L. and L. Greengard, "Debye sources and the numerical solution of the time harmonic Maxwell equations," Communications on Pure and Applied Mathematics, Vol. LXIII, 413-463, 2010.

51. Markkanen, J., C.-C. Lu, X. Cao, and P. Yla-Oijala, "Analysis of volume integral equations for scattering by high-contrast penetrable objects," IEEE Trans. Antennas Propag., Vol. 60, No. 5, 2367-2374, 2012.

52. Ubeda, E. and J. M. Rius, "New electric-magnetic field integral equation for the scattering analysis of perfectly conducting sharp-edged objects at very low or extremely low frequencies," 2010 IEEE Antennas and Propagation Society International Symposium (APSURSI), Toronto, Canada, Jul. 11-17, 2010.

53. Yla-Oijala, P., S. P. Kiminki, and S. Jarvenpaa, "Solving IBC-CFIE with dual basis functions," IEEE Trans. Antennas Propag., Vol. 58, No. 12, 3997-4004, 2010.

54. Cools, K., F. P. Andriulli, D. De Zutter, and E. Michielssen, "Accurate and conforming mixed discretization of the MFIE," IEEE Antennas Wirel. Propag. Lett., Vol. 10, 528-531, 2011.

55. Ubeda, E., J. M. Tamayo, and J. M. Rius, "Taylor-orthogonal basis functions for the discretization in method of moments of second kind integral equations in the scattering analysis of perfectly conducting or dielectric objects," Progress In Electromagnetics Research, Vol. 119, 85-105, 2011.

56. Yl¨a-Oijala, P., S. P. Kiminki, K. Cools, F. P. Andriulli, and S. Jarvenpa, "Mixed discretization schemes for electromagnetic surface integral equations," Internat. J. Num. Model.: Electronic Networks, Devices and Fields, Vol. 25, No. 5, 525-540, 2012.

57. Markkanen, J., P. Yl¨a-Oijala, and A. Sihvola, "Discretization of the volume integral equation formulations for extremely anisotropic materials," IEEE Trans. Antennas Propag., Vol. 60, No. 11, 5195-5202, 2012.

58. Yan, S. and J.-M. Jin, "Self-dual integral equations for electromagnetic scattering from IBC objects," IEEE Trans. Antennas Propag., Vol. 61, No. 11, 5533-5546, 2013.

59. Dault, D. L., N. V. Nair, J. Li, and B. Shanker, "The generalized method of moments for electromagnetic boundary integral equations," IEEE Trans. Antennas Propag., Vol. 62, No. 6, 3174-3188, 2014.

60. Ubeda, E., J. M. Rius, and A. Heldring, "Nonconforming discretization of the electric-field integral equation for closed perfectly conducting objects," IEEE Trans. Antennas Propag., Vol. 62, No. 8, 4171-4186, 2014.

61. Yla-Oijala, P., S. P. Kiminki, J. Markkanen, and S. Jarvenpaa, "Error-controllable and well-conditioned MoM solutions in computational electromagnetics: Ultimate surface integral equation formulation," IEEE Antennas Propag. Magaz., Vol. 55, No. 6, 310-331, 2013.

62. Sihvola, A., Electromagnetic Mixing Formulas and Applications, IEE Electromagnetic Wave Series 47, IEE, Hertfordshire, United Kingdom, 1999.

63. Hoppe, D. J. and Y. Rahmat-Samii, Impedance Boundary Conditions in Electromagnetics, Taylor & Francis, Washington, DC, 1995.

64. Wallen, H., I. V. Lindell, and A. Sihvola, "Mixed-impedance boundary conditions," IEEE Trans. Antennas and Propag., Vol. 59, No. 5, 1580-1586, 2011.

65. Lindell, I. V. and A. Sihvola, "Electromagnetic boundary conditions defined in terms of normal field components," IEEE Trans. Antennas Propag., Vol. 58, No. 4, 1128-1135, 2010.

66. Lindell, I. V., Methods for Electromagnetic Field Analysis, 2nd edition, IEEE Press, New York, 1995.

67. Yaghijan, A. D., "Augmented electric- and magnetic-field integral equations," Radio Science, Vol. 16, No. 6, 987-1001, 1981.

68. Yla-Oijala, P., M. Taskinen, and S. Jarvenpaa, "Analysis of surface integral equations in electromagnetic scattering and radiation problems," Engineering Analysis with Boundary Elements, Vol. 32, 196-209, 2008.

69. Yla-Oijala, P. and M. Taskinen, "Application of combined field integral equation for electromagnetic scattering by dielectric and composite objects," IEEE Trans. Antennas Propag., Vol. 53, No. 3, 1168-1173, 2005.

70. Harrington, R. F., "Boundary integral formulations for homogeneous material bodies," Journal of Electromagnetic Waves and Applications, Vol. 3, No. 1, 1-15, 1989.

71. Poggio, A. J. and E. K. Miller, "Integral equation solutions of three-dimensional scattering problems," Computer Techniques for Electromagnetics, R. Mittra (ed.), Pergamon Press, Oxford, U.K., 1973.

72. Medgyesi-Mitschang, L. N. and J. M. Putnam, "Integral equation formulations for imperfectly conducting scatterers," IEEE Trans. Antennas Propag., Vol. 33, No. 2, 206-214, 1985.

73. Markkanen, J., P. Yla-Oijala, and A. Sihvola, "Computation of scattering by DB objects with surface integral equation method," IEEE Trans. Antennas Propag., Vol. 59, No. 1, 154-161, 2011.

74. Kiminki, S. P., J. Markkanen, and P. Yla-Oijala, "Integral equation solution for the D’B’ boundary condition," IEEE Antennas Wirel. Propag. Lett., Vol. 9, 526-529, 2010.

75. Yla-Oijala, P., M. Taskinen, and J. Sarvas, "Surface integral equation method for general composite metallic and dielectric structures with junctions," Progress In Electromagnetic Research, Vol. 52, 81-108, 2005.

76. Volakis, J. L., "Alternative field representations and integral equations for modeling inhomogeneous dielectrics," IEEE Trans. Microw. Theory Techn., Vol. 40, 604-608, 1992.

77. Lu, C. C. and W. C. Chew, "A coupled surface-volume integral equation approach for the calculation of electromagnetic scattering from composite metallic and material targets," IEEE Trans. Antennas Propag., Vol. 48, No. 12, 1866-1868, 2000.

78. Harrington, R. F., Field Computation by Moment Methods, Macmillan, New York, 1968.

79. Wilton, D. R., Computational Methods, Chapter 1.5.5 in Scattering and Inverse Scattering in Pure and Applied Science, Roy Pick and Pierre Sabatier (eds.), 316–365, Elsevier, 2002.

80. Hsiao, G. C. and R. E. Kleinman, "Mathematical foundations for error estimation in numerical solutions of integral equations in electromagnetics," IEEE Trans. Antennas Propag., Vol. 45, No. 3, 316-328, 1997.

81. Bossavit, A., Computational Electromagnetism, Variational Formulations, Complementary, Edge Elements, Academic Press, San Diego, USA, 1998.

82. Monk, P., Finite Element Methods for Maxwell’s Equations, Oxford Science Publications, Clarendon Press, Oxford, 2003.

83. Buffa, A., M. Costabel, and C. Schwab, "Boundary element methods for Maxwell’s equations on non-smooth domains," Numerische Mathematic, Vol. 92, 679-710, 2002.

84. Warnick, K., Numerical Analysis for Electromagnetic Integral Equations, Artech House, 2008.

85. Wilton, D. R., S. M. Rao, A. W. Glisson, D. H. Schaubert, O. M. Al-Bundak, and C. M. Butler, "Potential integrals for uniform and linear source distributions on polygonal and polyhedral domains," IEEE Trans. Antennas Propag., Vol. 32, No. 3, 276-281, 1984.

86. Graglia, R. D., "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 Propag., Vol. 41, No. 9, 1448-1455, 1993.

87. Yla-Oijala, P. and M. Taskinen, "Calculation of CFIE impedance matrix elements with RWG and nxRWG functions," IEEE Trans. Antennas Propag., Vol. 51, No. 8, 1837-1848, 2003.

88. Jarvenpaa, S., M. Taskinen, and P. Yla-Oijala, "Singularity subtraction technique for high-order polynomial vector basis functions on planar triangles," IEEE Trans. Antennas Propag., Vol. 54, No. 1, 42-49, 2006.

89. Khayat, M. A. and D. R. Wilton, "Numerical evaluation of singular and near-singular potential integrals," IEEE Trans. Antennas Propag., Vol. 53, No. 10, 3180-3190, 2005.

90. Polimeridis, A. G. and T. V. Yioultsis, "On the direct evaluation of weakly singular integrals in Galerkin mixed potential integral equation formulations," IEEE Trans. Antennas Propag., Vol. 56, No. 9, 3011-3019, 2008.

91. Van Beurden, M. C. and S. J. L. van Eijndhoven, "Gaps in present discretization schemes for domain integral equations," International Conference on Electromagnetics in Advanced Applications, ICEAA 2007, Torino, 2007.

92. Van Beurden, M. C. and S. J. L. van Eijndhoven, "Well-posedness of domain integral equations for a dielectric object in homogeneous background," J. Eng. Math., Vol. 62, 289-302, 2008.

93. Schaubert, D., D. Wilton, and A. Glisson, "A tetrahedral modeling method for electromagnetic scattering by arbitrarily inhomogeneous dielectric bodies," IEEE Trans. Antennas Propag., Vol. 32, No. 1, 77-85, 1984.

94. Nedelec, J. C., "Mixed finite elements in R3," Numerische Mathematik, Vol. 35, 315-341, 1980.

95. Christiansen, S. H. and J.-C. Nedelec, "A preconditioner for the electric field integral equation based on Calderon formulas," SIAM J. Numerical Anal., Vol. 40, No. 3, 459-485, 200.

96. Buffa, A. and S. H. Christiansen, "A dual finite element complex on the barycentric refinement," Math. Comput., Vol. 76, No. 260, 1743-1769, 2007.

97. Kiminki, S. P., I. Bogaert, and P. Yla-Oijala, "Dual basis for the fully linear LL functions," 2012 IEEE International Symposium on Antennas and Propagation and USNC-URSI National Radio Science Meeting, Chicago, Illinois, USA, Jul. 8-14, 2012.

98. Contopanagos, H., B. Dembart, M. Epton, J. J. Ottusch, V. Rokhlin, J. L. Fisher, and S. M. Wandzura, "Well-conditioned boundary integral equations for three-dimensional electromagnetic scattering," IEEE Trans. Antennas Propag., Vol. 50, No. 12, 1824-1830, 2002.

99. Li, M. and W. C. Chew, "Applying divergence-free condition solving the volume integral equations," Progress In Electromagnetic Research, Vol. 57, 311-333, 2006.

100. Markkanen, J., P. Yla-Oijala, and S. Jarvenpaa, "Volume integral equation formulations in computational electromagnetics," International Conference on Electromagnetics in Advanced Applications, Torino, Italy, Sep. 9-13, 2013.

101. Costabel, M., E. Darrigrand, and H. Sakly, "Essential spectrum of the volume integral operator in electromagnetic scattering by a homogeneous body," Comptes Rendus Mathematique, Vol. 350, No. 3–4, 193-197, 2012.

102. Hiptmair, R. and C. Schwab, "Natural boundary element methods for the electric field integral equation on polyhedra," SIAM J. Numer. Anal., Vol. 40, No. 1, 66-86, 2002.

103. Buffa, A., R. Hiptmair, T. von Petersdorff, and C. Schawb, "Boundary element methods for Boundary element methods for Maxwell transmission problems in Lipschitz domains," Numer. Math., Vol. 95, 459-485, 2003.

104. Muller, C., Foundations of the Mathematical Theory of Electromagnetic Waves, Springer, Berlin, 1969.

105. Liu, Y. A. and W. C. Chew, "Stability of surface integral equation for left-handed materials," IET Microw. Antennas Propag., Vol. 1, No. 1, 84-89, 2007.

106. Yla-Oijala, P. and M. Taskinen, "Improving conditioning of electromagnetic surface integral equations using normalized field quantities," IEEE Trans. Antennas Propag., Vol. 55, No. 1, 178-185, 2007.

107. Wilton, D. R. and A. W. Glisson, "On improving stability of the electric field integral equation at low frequencies," Proceedings of URSI Radio Science Meeting, Vol. 24, Los Angeles, CA, Jun. 1981.

108. Mautz, J. R. and R. F. Harrington, "An E-field solution for a conducting surface small or comparable to the wavelength," IEEE Trans. Antennas Propag., Vol. 32, No. 4, 330-339, 1984.

109. Wu, W.-L., A. W. Glisson, and D. Kajfez, "A study of two numerical solution procedures for the electric field integral equation at low frequency," Appl. Comput. Soc. J., Vol. 10, No. 3, 69-80, 1995.

110. Yla-Oijala, P. and M. Taskinen, "Well-conditioned M¨uller formulation for electromagnetic scattering by dielectric objects," IEEE Trans. Antennas Propag., Vol. 53, No. 10, 3316-332, 2005.

111. Vecchi, G., "Loop-star decomposition of basis functions in the discretization of the EFIE," IEEE Trans. Antennas Propag., Vol. 47, No. 2, 339-346, 1999.

112. Andriulli, F. P., A. Tabacco, and G. Vecchi, "Solving the EFIE at low frequencies with a conditioning that grows only logarithmically with the number of unknowns," IEEE Trans. Antennas Propag., Vol. 58, No. 5, 1614-1623, 2010.

113. Chen, S. Y., W. C. Chew, J. M. Song, and J.-S. Zhao, "Analysis of low-frequency scattering from penetrable scatterers," IEEE Trans. Geosc. Remote Sensing, Vol. 39, No. 4, 726-735, 2001.

114. Yla-Oijala, P., S. P. Kiminki, and S. Jarvenpa, "Electromagnetic surface integral equation representations in terms of scalar functions," International Conference on Electromagnetics in Advanced Applications, Torino, Italy, Sep. 9-13, 2013.

115. Gulzow, V., "An integral equation method for the time-harmonic Maxwell equations with boundary conditions for the normal components," J. Integral Eq., Vol. 1, No. 3, 1988.

116. Stephanson, M. B. and J.-F. Lee, "Preconditioned electric field integral equation using Calderon identities and dual loop/star basis functions," IEEE Trans. Antennas Propag., Vol. 57, No. 4, 1274-1279, 2009.

117. Bagci, H., F. P. Andriulli, K. Cools, F. Olyslager, and E. Michielssen, "A Caldern multiplicative preconditioner for the combined field integral equation," IEEE Trans. Antennas Propag., Vol. 57, No. 10, 3387-3392, 2009.

118. Cools, K., F. P. Andriulli, and E. Michielssen, "A Calderon multiplicative preconditioner for the PMCHWT integral equation," IEEE Trans. Antennas Propag., Vol. 59, No. 12, 4579-4587, 2011.

119. Begheim, Y., K. Cools, F. P. Andriulli, D. De Zutter, and E. Michielssen, "A Caldern multiplicative preconditioner for the PMCHWT equation for scattering by chiral objects," IEEE Trans. Antennas Propag., Vol. 60, No. 9, 4239-4248, 2012.

120. Jarvenpaa, S. and P. Yla-Oijala, "A global interpolator with low sample rate for multilevel fast multipole algorithm," IEEE Trans. Antennas Propag., Vol. 61, No. 3, 1291-1300, 2013.

121. Gumerov, N. A. and R. Duraiswami, Fast Multipole Methods for the Helmholtz Equation in Three Dimensions, Elsevier, Amsterdam, The Netherlands, 2006.

122. Jarvenpa, S., J. Markkanen, and P. Yla-Oijala, "Broadband multilevel fast multipole algorithm for electric-magnetic current volume integral equation," IEEE Trans. Antennas Propag., Vol. 61, No. 8, 4393-4397, 2013.

123. Jiang, L. J. and W. C. Chew, "Low-frequency fast inhomogeneous plane-wave algorithm (LFFIPWA)," Microw. Opt. Techn. Lett., Vol. 40, No. 2, 117-122, 2004.

124. Darve., E. and P. Have, "A fast multipole method for Maxwell’s equations stable at all frequencies," Phil. Trans. Royal Society of London A, Vol. 362, No. 1816, 603-628, Mar. 2004.

125. Wallen, H. and J. Sarvas, "Translation procedures for broadband MLFMA," Progress In Electromagnetic Research, Vol. 55, 47-78, 2005.

126. Koc, S., J. Song, and W. C. Chew, "Error analysis for the numerical evaluation of the diagonal Error analysis for the numerical evaluation of the diagonal," SIAM J. Anal., Vol. 36, No. 3, 906-921, 1999.

127. Darve, E., "The fast multipole method: Numerical implementation," J. Comput. Phys., Vol. 160, 195-240, 2000.

128. Sarvas, J., "Performing interpolation and anterpolation entirely by fast Fourier transform in the 3-D multilevel fast multipole algorithm," SIAM J. Numer. Anal., Vol. 41, No. 6, 2180-2196, 2003.

129. Cecka, C. and E. Darve, "Fourier-based fast multipole method for the Helmholtz equation," SIAM J. Sci. Comput., Vol. 35, No. 1, A79-A103, 2013.

130. Jarvenpaa, S. and P. Yla-Oijala, "Multilevel fast multipole algorithm with local and global interpolators," 2013 IEEE International Symposium on Antennas and Propagation and USNCURSI National Radio Science Meeting, Orlando, Florida, USA, Jul. 7-13, 2013.

131. Ergul, O. and L. Grel, "A hierarchical partitioning strategy for an efficient parallelization of the multilevel fast multipole algorithm," IEEE Trans. Antennas Propag., Vol. 57, No. 6, 1740-1750, 2009.

132. Fostier, J. and F. Olyslager, "An asynchronous parallel MLFMA for scattering at multiple dielectric objects," IEEE Trans. Antennas Propag., Vol. 56, No. 8, 2346-2355, 2008.

133. Li, M. K. and W. C. Chew, "Wave-field interaction with complex structures using equivalence principle algorithm," IEEE Trans. Antennas Propag., Vol. 55, No. 1, 130-138, 2007.

134. Lancellotti, V., B. P. de Hon, and A. G. Tijhuis, "An eigencurrent approach to the analysis of electrically large 3-D structures using linear embedding via Green’s operators," IEEE Trans. Antennas Propag., Vol. 57, No. 11, 3575-3585, 2009.

135. Peng, Z., X.-C. Wang, and J.-F. Lee, "Integral equation based domain decomposition method for solving electromagnetic wave scattering from non-penetrable objects," IEEE Trans. Antennas Propag., Vol. 59, No. 9, 3328-3338, 2011.

136. Georgieva, N. K., S. Glavic, M. H. Bakr, and J. W. Bandler, "Feasible adjoint sensitivity technique for EM design optimization," IEEE Trans. Microw. Theory Techn., Vol. 50, No. 12, 2751-2758, 2002.

137. Nikolova, N. K., J. Zhu, D. Li, M. H. Bakr, and J. W. Bandler, "Sensitivity analysis of network parameters with electromagnetic frequency-domain simulators," IEEE Trans. Microw. Theory Techn., Vol. 54, No. 2, 670-681, 2006.

138. Toivanen, J. I., R. A. E. Makinen, S. Jarvenpaa, P. Yla-Oijala, and J. Rahola, "Electromagnetic sensitivity analysis and shape optimization using method of moments and automatic differentiation," IEEE Trans. Antennas Propag., Vol. 57, No. 1, 168-175, 2009.

139. Kataja, J. and J. I. Toivanen, "On shape differentiation of discretized electric field integral equation," Eng. Anal. Boundary Elem., Vol. 37, No. 9, 1197-1203, 2013.

140. Kataja, J., S. Jarvenpaa, and R. A. E. Makinen, "Shape sensitivity analysis of electrically large metallic electromagnetic scatterers," Opt-i, An International Conference on Engineering and Applied Sciences Optimization, Kos Island, Greece, Jun. 4-6, 2014.

Download Full Article (968) View Full Article volume
The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.