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CEM methods in R.F and microwave engineering in the context of parameters that influence the outcome of modeling

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Abstract

The starting point toward modeling of a given electromagnetic (EM) problem is to know the modeling constraints/features of different modeling tools, and hence figure out if they are compatible to meet the intended objectives. In the face of popularity of some modeling tools, due to either marketing strategy or researcher bias, and compounded by lack of empirical data toward bench marking different methods for comparison, an intuitive choice will compromise accuracy, speed and efficiency. In this paper, an attempt is made to present the commonly used computational electromagnetic (CEM) methods in the context of basic parameters and their limiting values that influence the modeling outcome. A prospective researcher can make a checklist of these parameters and customize them fit into the given EM problem. This facilitates the selecting of an optimal method from the many that are available. This is important to mitigate the problem of computation cost that creep in the design/synthesis emanating from wrong choice of the modeling tool, and also, in the perspective of research and development, the life cycle is reduced that add to the economic viability of the modeled prototype. For an entry-level researcher, some level of proficiency in the CEM methods and EM simulators based on these methods enhance the prospect of employment in radio-frequency and microwave industry/research.

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References

  1. A. Sommerfeld, Electrodynamics: Lectures on Theoretical Physics, vol. 3 (Academic Press, Cambridge, 2013)

    Google Scholar 

  2. J.A. Stratton, Electromagnetic Theory (McGraw-Hill Book Company, New York, 1941)

    Google Scholar 

  3. C. Hebedeon, C. Munteanu, Numerical modeling of microstrip patch antenna. ACTA Electrotehnica 51(4), 281–284 (2010)

    Google Scholar 

  4. H.Z. Zhang et al., Monopole to slot antenna coupling analysis for resonant and higher order harmonics via UTD, in 2013 IEEE Antenna and Propagation Society International Symposium(APSURS), (2013), pp.1068–1069

  5. A. Grebennikov et al., Broadband RF and Microwave Amplifiers (CRC Press, Taylor and Francis group, Boca Raton, 2016)

    Google Scholar 

  6. A. Chinig et al., Design of microstrip diplexer and triplexer using open loop resonators. J. Microwave Opto-Electron. Electromagnet. Appl. 15(2), 65–80 (2016)

    Google Scholar 

  7. S.E.Jasim et al., Design of 2.5 GHz broad bandwidth microwave band pass filter at operating frequency of 10 GHz using HFSS. in IOP Conference Series: Material Science and Engineering, (vol. 342, 2018)

  8. U. Jakobus et al., Overview of recent extensions in FEKO with regard to MLFMM and Cable coupling, EM Software & Systems-S.A (Pty) Ltd., Techno park, Stellenbosch 7600, and EM Software

  9. M. Schoeman et al., Recent advances to the FEKO integrated cable harness modeling tool, in 2007 2nd International ITG Conference on Antennas, (2007)

  10. Y.N. Liu et al., Fast and accurate calculation of electromagnetic scattering and radiation fields. IEEE Trans. Antenna Propagat. 67(11), 1–6 (2019)

    ADS  Google Scholar 

  11. O.B. Anatoliy et al., Time domain simulation technique for antenna transient radiation, reception and scattering, ultra-wideband, short pulse electromagnetics. in by P.D. Smith, S.R. Cloude, Klumer Academic/Plenum Publisher, (2002)

  12. D. Mirkovic et al., Polarimetric weather radar calibration by computational electromagnetics. Appl. Comput. Electromagn. Soc. J. 34(2), 342–346 (2019)

    Google Scholar 

  13. P. Zuo et al., A novel electromagnetic bandgap design applied for suppression of printed circuit board electromagnetic radiation. Int. J. RF Microwave Comput. Aided Eng. 30(1), 990 (2020)

    Google Scholar 

  14. Y.S. Xiao et al., An equivalent modeling method for the radiated electromagnetic interference of printed circuit board on near field scanning. ACES J. 34(5), 784–790 (2019)

    Google Scholar 

  15. E. Tziris et al., Optimized planar elliptical dipole antenna for UWB EMC applications. IEEE Trans. Electromagn. Compat. 61(4), 1377–1383 (2019)

    Google Scholar 

  16. F. Yang, Y. Rahmat-Samii, Surface Electromagnetics: with Applications in Antenna, Microwave and Optical Engineering (Cambridge University Press, Cambridge, 2019)

    Google Scholar 

  17. L. Jiang et al., Terahertz high and near-zero refractive index metamaterials by double layer metal ring microstructure. Opt. Laser Technol. 123, 10594 (2019)

    Google Scholar 

  18. S. Xie et al., Recent progress in electromagnetic wave absorption buildings materials. J. Build. Eng. 27, 1–14 (2020)

    Google Scholar 

  19. H. Lai, Exposure to static and extremely low frequency electromagnetic fields and cellular free radicals. Electromagn. Biol. Med. 38(4), 231–248 (2019)

    Google Scholar 

  20. D.B. Davidson, Computational Electromagnetics for RF and Microwave Engineering (Cambridge University Press, New York, 2005)

    Google Scholar 

  21. A. Taflove, S.C. Hagness, Computational Electromagnetics: The Finite Difference Time-Domain Method, 2nd edn. (Artech House, Boston, 2000)

    Google Scholar 

  22. G. Meunire, The Finite Element Method for Electromagnetic Modeling (Wiley, Hoboken, 2003)

    Google Scholar 

  23. K.S. Kunz, R.J. Luebbers, Finite Difference Time Domain Method for Electromagnetics (CRC Press, Taylor & Francis Group, Boca Raton, 2009)

    Google Scholar 

  24. M.N.O. Sadiku, Numerical Techniques in Electromagnetics with Matlab, 3rd edn. (CRC Press, Taylor & Francis Group, Boca Raton, 2009)

    Google Scholar 

  25. R. Paknys, Applied Frequency-Domain Electromagnetics, 3rd edn. (Wiley, Hoboken, 2016)

    Google Scholar 

  26. W.C. Gibson, The Method of Moments in Electromagnetics, 2nd edn. (CRC Press, Taylor & Francis Group, Boca Raton, 2015)

    Google Scholar 

  27. Aakash A. Bhatt, K. Sankaran, How to model Electromagnetic Problems without using Vector Calculus and Differential Equations? IETE J. Edu. 59(2), 85–92 (2018)

    Google Scholar 

  28. K. Sankaran, Recent trends in computational electromagnetics for defense applications. Defense Sci. J. 69(1), 65–73 (2019)

    Google Scholar 

  29. K. Sankaran, Are You Using the Right Tools in Computational Electromagnetics? (Engineering Reports. Wiley, Hoboken, 2019), pp. 1–19. https://doi.org/10.1002/eng2.12041

    Book  Google Scholar 

  30. S. Park et al., Lessons from validation of computational electromagnetics computer modeling and simulation based on IEEE standard 1597, Paper presented at IEEE MTT-S International Microwave Symposium (IMS), (Honolulu, 2017)

  31. A.P. Duffy et al., Feature selective validation (FSV) for validation of computational electromagnetics (CEM) Part I-the FSV method. IEEE Trans. Electromagn. Compat. 48(3), 449–459 (2006)

    MathSciNet  Google Scholar 

  32. A. Orlandi et al., Feature selective validation (FSV) for validation of computational electromagnetics (CEM). Part II-assessment of FSV performance. IEEE Trans. Electromagn. Compat. 48(3), 460–467 (2006)

    Google Scholar 

  33. IEEE Standard for Validation of Computational Electromagnetics, Computer Modeling and Simulations, IEEE Std 1597.1-2008. (2008)

  34. IEEE Recommended Practice for Validation of Computational Electromagnetics, Computer Modeling and Simulations, IEEE Std 1597.2-2010. (2011)

  35. D.S. Burnett, Finite Element Analysis (Addison-Wesley, Reading, 1987)

    Google Scholar 

  36. R. Feynman, Lectures in Physics, vol. 2 (Addison-Wesley, Boston, 1964)

    Google Scholar 

  37. L.Marro, Méthodes de Réduction de la largeur de bande et du profil efficace des matrices creuses. Ph.D. thesis, Université de Nice, (1980)

  38. P. George, Automatic Mesh Generation: Application to Finite Element Methods (Wiley, Paris, 1991)

    Google Scholar 

  39. O.C. Zienkiewicz, R.L. Taylor, The Finite Element Method, 5th edn. (Butterworth-Heinemann, Boston, 2000), p. 401

    Google Scholar 

  40. D.W. Pepper, J.C. Heinrich, The Finite Element Method, Basic Concepts and Application (Taylor & Francis Publishing, Hemisphere Publishing C, Milton Park, 1992)

    Google Scholar 

  41. M. Okoniewski, E. Okoniewska, M. Stuchly, Three-dimensional subgridding algorithm for FDTD. IEEE Trans. Antennas Propag. 45(3), 422–429 (1997)

    ADS  Google Scholar 

  42. B. Denecker, F. Olyslager, L. Knockaert, D. De Zutter, Generation of FDTD subcell equations by means of reduced order modeling. IEEE Trans. Antennas Propag. 51(8), 1806–1817 (2003)

    ADS  Google Scholar 

  43. K. Xiao, D.J. Pommerenke, J.L. Drewniak, A three-dimensional FDTD subgridding algorithm with separated temporal and spatial interfaces and related stability analysis. IEEE Trans. Antennas Propag. 55(7), 1981–1990 (2007)

    ADS  MathSciNet  Google Scholar 

  44. S.M. Rao, Time domain electromagnetics, Academic Press in Engineering, 1st edn. (Academic Press, Cambridge, 1999)

    Google Scholar 

  45. P. Robert, Applied Frequency-Domain Electromgnetics, 1st edn. (Wiley, Hoboken, 2016)

    Google Scholar 

  46. R. Maier, D. Peterseim, Explicit computational wave propagation in micro heterogeneous media. BIT Numer. Math. 59(2), 443–462 (2018)

    MathSciNet  Google Scholar 

  47. Y.J. Sheng et al., Efficient analysis of ferrite R.F Devices by explicit time domain methods in unstructured meshes. IEEE Trans. Magnet. 54(6), 1–6 (2016)

    Google Scholar 

  48. D. Soares, A novel family of explicit time marching techniques for structural dynamics and wave propagation models. Comput. Methods Appl. Mech. Eng. 311, 838–855 (2016)

    ADS  MathSciNet  Google Scholar 

  49. A. Samimi, M. Rodriguez, N. Dupree, R. Moore, J.J. Simpson, The application of global 3-D FDTD Earth-ionosphere models to VLF propagation: comparison with LWPC. Paper presented at: IEEE AP-S International Symposium and USNC/URSI National Radio Science Meeting, 2016; Fajardo, Puerto Rico

  50. H. Vincenti, J.-L. Vay, Ultrahigh-order Maxwell solver with extreme scalability for electromagnetic PIC simulations of plasmas. Comput. Phys. Commun. 228, 22–32 (2018)

    ADS  Google Scholar 

  51. R. Courant, K. Friedrichs, H. Lewy, On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11(2), 215–234 (1967)

    ADS  MathSciNet  Google Scholar 

  52. L. Xing et al., A New implicit hybridizable discontinuous galerkin time-domain method for solving the 3-D electromagnetic problems. Appl. Math. Lett. 93, 124–130 (2019)

    MathSciNet  Google Scholar 

  53. J.J. Ottusch, J.L. Visher, Novel implicit method for faster modeling of low frequency electromagnetic problems in the time domain. in 2017 Progress in Electromagnetic Research Symposium-Fall(PIERS-FALL), (2017), pp. 1795–1800

  54. J. Chen, A reviw of hybrid implicit-explicit finite difference time domain methods. J. Comput. Phys. 363, 256–267 (2018)

    ADS  MathSciNet  Google Scholar 

  55. B. Zhu et al., A hybrid finite element/finite difference method with implicit-explicit time stepping scheme fpr Maxwell’s equations. in 2011 IEEE International Conference on Microwave Technology and Computational Electromagnetic, (2011), pp. 481–484

  56. H.A. Lorentz, The Theory of Electrons and Its Applications to the Phenomena of Light and Radiant Heat (Dover Books, Mineola, 1915)

    Google Scholar 

  57. J.H. Greene, A. Taflove, General vector auxiliary differential equation finite-difference time-domain method for nonlinear optics. Opt. Express 14(18), 8305–8310 (2006)

    ADS  Google Scholar 

  58. S.C. Hagness, R.M. Joseph, A. Taflove, Subpicosecond electrodynamics of distributed Bragg reflector microlasers: results from finite difference time domain simulations. Radio Sci. 31(4), 931–941 (1996)

    ADS  Google Scholar 

  59. A.S. Nagra, R.A. York, FDTD analysis of wave propagation in nonlinear absorbing and gain media. IEEE Trans. Antennas Propag. 46(3), 334–340 (1998)

    ADS  Google Scholar 

  60. S.H. Chang, A. Taflove, Finite-difference time-domain model of lasing action in a four-level two-electron atomic system. Opt. Express 12(16), 3827–3833 (2004)

    ADS  Google Scholar 

  61. Y. Huang, S.T. Ho, Computational model of solid-state, molecular, or atomic media for FDTD simulation based on a multi-level multi-electron system governed by Pauli exclusion and Fermi-Dirac thermalization with application to semiconductor photonics. Opt. Express 14(8), 3569–3587 (2006)

    ADS  Google Scholar 

  62. A.A. Al-Jabr, B.S. Ooi, M.A. Alsunaidi, An FDTD algorithm for simulation of EM waves propagation in laser with static and dynamic gain models. in Paper presented at: Saudi International Electronics, Communications and Photonics Conference, (Fira, Greece, 2013)

  63. A. Samimi, J.J. Simpson, Parallelization of 3-D global FDTD Earth-ionosphere waveguide models at resolutions on the order of 1% km and higher. IEEE Antennas Wirel. Propag. Lett. 15, 1959–1962 (2016)

    ADS  Google Scholar 

  64. W.C. Chew, J.-M. Jin, E. Michielssen, J. Song, Fast and Efficient Algorithms in Computational Electromagnetics (Artech House, Norwood, 2001)

    Google Scholar 

  65. G. Green, An Essay on the Application of Mathematical Analysis to the Theories of Electricity and Magnetism (T. Wheelhouse, Nottingham, 1828)

    Google Scholar 

  66. W.C. Chew, M.S. Tong, B. Hu, Integral Equation Methods for Electromagnetic and Elastic Waves, 1st edn. (Morgan & Claypool, San Rafael, 2009)

    Google Scholar 

  67. T. Takahashi, P. Coulier, E. Darve, Application of the inverse fast multipole method as a preconditioner in a 3D Helmholtz boundary element method. J. Comput. Phys. 341, 406–428 (2017)

    ADS  MathSciNet  Google Scholar 

  68. U.M. Gür, B. Karaosmanogglu, O. Ergül (2017) Fast-multipole-method solutions of new potential integral equations. in Paper presented at: 4th International Electromagnetic Compatibility Conference (EMC Turkiye), (Ankara, Turkey, 2017)

  69. R. Yokota, H. Ibeid, D. Keyes, Fast multipole method as a matrix-free hierarchical low-rank approximation, in Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing, ed. by T. Sakurai, S.-L. Zhang, T. Imamura, Y. Yamamoto, Y. Kuramashi, T. Hoshi (Springer, Cham, 2017), pp. 267–286

    Google Scholar 

  70. S.N. Makarov, G.M. Noetscher, T. Raij, A. Nummenmaa, A quasi-static boundary element approach with fast multipole acceleration for high-resolution bioelectromagnetic models. IEEE Trans. Biomed. Eng. 65(12), 2675–2683 (2018)

    Google Scholar 

  71. R.P. Federonko, A relaxation method for solving elliptic equation. USSR Comput. Math. Math. Phys. 1(4), 1092–1096 (1962)

    Google Scholar 

  72. O. Axelsson, V.A. Barker, Finite Element Solution of Boundary Value Problems: Theory and Computation, 1st edn. (Academic Press, Cambridge, 1984)

    Google Scholar 

  73. S. Jaffard, Wavelet methods for fast resolution of elliptic problems. SIAM J. Numer. Anal. 29(4), 965–986 (1992)

    MathSciNet  Google Scholar 

  74. R.L. Wagner, W.C. Chew, A study of wavelets for the solution of electromagnetic integral equations. IEEE Trans. Antennas Propag. 43(8), 802–810 (1995)

    ADS  Google Scholar 

  75. Sankaran K.Accurate Domain Truncation Techniques for Time-Domain Conformal Methods[PhD thesis]. Zürich, Switzerland: ETH; 2007.https://doi.org/10.3929/ethz-a-005514071

  76. R. Feynman, Lectures in Physics, vol. 3 (Addison-Wesley, Boston, 1965)

    Google Scholar 

  77. I.V. Lindell, A. Sihvola, Electromagnetic Boundaries with PEC/PMC equivalence. Prog. Electromagn. Res. Lett. 61, 119–123 (2016)

    Google Scholar 

  78. Yan S, Jin JM. A self-dual integral equation for solving EM scattering from PEC, PMC, and IBC objects. Paper Presented at: Antennas and Propagation Society International Symposium, APSURSI, (Orlando, FL, 2013)

  79. T.B.A. Senior, Impedance boundary conditions for imperfectly conducting surfaces. Appl. Sci. Res. Sect. B. 8(1), 418 (1960)

    MathSciNet  Google Scholar 

  80. T.B.A. Senior, J.L. Volakisa, Generalized impedance boundary conditions in scattering. Proc. IEEE 79(10), 1413–1420 (1991). https://doi.org/10.1109/5.104216

    Article  Google Scholar 

  81. L. Xiangang et al., Taming the electromagnetic boundaries via metasurfaces: from theory and fabrication to functional devices. Int. J. Antennas Propagat. (2015). https://doi.org/10.1155/2015/204127

    Article  Google Scholar 

  82. I. Muench et al., Periodic boundary conditions for the simulation of 3d domain patterns in tetragonal ferroelectric material. Arch Mech 89, 955–972 (2019). https://doi.org/10.1007/s00419-018-1411-9

    Article  Google Scholar 

  83. I.D. Mayergoyz et al., A new time-domain approach to the analysis of scattering problems. IEEE Trans. Magnet. 38(2), 327–332 (2002). https://doi.org/10.1109/20.99089

    Article  ADS  Google Scholar 

  84. M. Zhao et al., Time-domain stability of artificial boundary condition coupled with finite element for dynamic and wave problems in unbounded media. Int. J. Comput. Methods 15(3), 1–33 (2018)

    ADS  Google Scholar 

  85. I. Orlanski, A simple boundary condition for unbounded hyperbolic flows. J. Comput. Phys. 21, 251–269 (1976)

    ADS  Google Scholar 

  86. S.H. Schot, Eighty Years of Sommerfeld’s radiation condition. Historia Mathematica 19, 385–401 (1992)

    MathSciNet  Google Scholar 

  87. M. Ruyan, A survey of non-local boundary value problems. Appl. Math. E-notes 7, 257–279 (2007)

    MathSciNet  Google Scholar 

  88. G.J. Fix, S.P. Marin, Variational methods for underwater acoustic problems. J. Comput. Phys. 28, 253–270 (1978)

    ADS  MathSciNet  Google Scholar 

  89. L. Ting, M.J. Miksis, Exact boundary condition for scattering problems. J. Acoust. Soc. Am. 80(6), 1825–1827 (1986)

    ADS  Google Scholar 

  90. D. Givoli, J.B. Keller, Non-reflecting boundary condition for elastic waves. Wve motion 12, 261–279 (1990)

    Google Scholar 

  91. M.J. Grote, J.B. Keller, Exact non-reflecting boundary condition for the time dependent wave equation. SIAM. J. Appl. Math. 55, 280–297 (1995)

    MathSciNet  Google Scholar 

  92. I.L. Sofronov, Artificial boundary conditions of absolute transparency for two-and-three dimensional external time-dependent scattering problems. European J. of Appl. Math. 9, 561–588 (1998)

    MathSciNet  Google Scholar 

  93. I.L. Safronov, Truncated Transparent boundary conditions. arXiv:1609.09280. (2016)

  94. X. Antoine et al., A review of transparent and artificial boundary techniques for linear and non-linear Schrodinger equations. Commun. Comput. Phys. 4(4), 729–796 (2008)

    MathSciNet  Google Scholar 

  95. J.F. Mennemann, J. Jungel, Perfectly matched layers versus discrete boundary conditions in quantum device simulations. J. Comput. Phys. 275, 1–24 (2014)

    ADS  MathSciNet  Google Scholar 

  96. B. Alpert et al., Rapid evaluation of non-reflecting boundary kernels for time domain wave propagation. SIAM J. Numer. Anal. 37, 1138–1164 (2000)

    MathSciNet  Google Scholar 

  97. B. Alpert et al., Non-reflecting boundary conditions for the time-dependent wave equation. J. Comput. Phys. 180, 270–296 (2002)

    ADS  MathSciNet  Google Scholar 

  98. S. Jiang, L. Greengard, Efficient representation of non-reflecting boundary conditions for the time dependent Schrodinger equation in two dimensions. Commun. Pure Appl. Math. A J. Issued Courant Institute Math. Sci. 61, 261–288 (2008)

    Google Scholar 

  99. R. Clayton, B. Engquist, Absorbing boundary conditions for acoustic and elastic wave equations. Bull. Siesmol. Soc. Am. 67, 1529–1540 (1977)

    Google Scholar 

  100. B. Engquist, A. Majda, Absorbing boundary conditions for numerical simulation of waves. Proc. Nat. Acad. Sci. 74, 1765–1766 (1977)

    ADS  MathSciNet  Google Scholar 

  101. B. Engquist, A. Majda, Radiation boundary conditions for acoustic and elastic wave calculations. Comm. Pure. Appl. Math. 32, 313–357 (1979)

    MathSciNet  Google Scholar 

  102. A. Bayliss, E. Turkel, Radiation boundary condition for wave like equations. Commun. Pure Appl. Math. 33, 707–725 (1980)

    ADS  MathSciNet  Google Scholar 

  103. R.L. Higdon, Absorbing boundary conditions for difference approximations to the multidimensional wave equations. Math. Comput. 47, 437–459 (1986)

    MathSciNet  Google Scholar 

  104. T. Hagstrom, S. Hariharan, A formulation of asymptotic and exact boundary conditions using local operators. Appl. Numer. Math. 27, 403–416 (1998)

    MathSciNet  Google Scholar 

  105. P.-b. Zhou, Numerical Analysis of EM Fields, Electric Energy Systems and Engineering Series, 1st edn. (Springer, Berlin, 1993)

    Google Scholar 

  106. D. Givoli, No-reflecting boundary conditions. J. Comput. Phys. 94, 1–29 (1991)

    ADS  MathSciNet  Google Scholar 

  107. D. Givoli, High-order local non-reflecting boundary conditions: a review. Wave Motion 39, 319–326 (2004)

    MathSciNet  Google Scholar 

  108. S.V. Tsynkov, Numerical solution of problems on unbounded domains: a review. Appl. Numer. Math. 27, 465–532 (1998)

    MathSciNet  Google Scholar 

  109. D. Gordon, R. Gordon, E. Turkel, Compact high order schemes with gradient-direction derivatives for absorbing boundary conditions. J. Comput. Phys. 297, 295–315 (2015)

    ADS  MathSciNet  Google Scholar 

  110. J.P. Bérenger, A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114(2), 185–200 (1994)

    ADS  MathSciNet  Google Scholar 

  111. J.P. Berenger, Three-dimensional perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 127(2), 363–379 (1996)

    ADS  MathSciNet  Google Scholar 

  112. D.S. Katz, E.C. Thiele, A. Taflove, Validation and extension to three dimensions of the Berenger PML absorbing boundary condition for FDTD meshes. IEEE Microw. Guided Wave Lett. 4(8), 268–269 (1994)

    Google Scholar 

  113. W.C. Chew, W.H. Weedon, A 3-D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. Microwave Opt. Technol. Lett. 7(13), 599–604 (1994)

    ADS  Google Scholar 

  114. D. Komatitsch, J. Tromp, A perfectly matched layer absorbing boundary condition for the second-order seismic wave equation. Geophys. J. Int. 154, 146–153 (2003)

    ADS  Google Scholar 

  115. F. Collino, P. Monk, The perfectly matched layer in curvilinear coordinates. SIAM J. Sci. Comput. 19, 2061–2090 (1998)

    MathSciNet  Google Scholar 

  116. D. Appelö, T. Hagstrom, G. Kreiss, Perfectly matched layers for hyperbolic systems: general formulation, well-posedness, and stability. SIAM J. Appl. Math. 67, 1–23 (2006)

    MathSciNet  Google Scholar 

  117. A. Nissen, G. Kreiss, An optimized perfectly matched layer for the Schrödinger equation. Commun. Comput. Phys. 9, 147–179 (2011)

    MathSciNet  Google Scholar 

  118. S. Abarbanel, D. Gottlieb, A mathematical analysis of the PML method. J. Comput. Phys. 134, 357–363 (1997)

    ADS  MathSciNet  Google Scholar 

  119. K. Sankaran, C. Fumeaux, R. Vahldieck, Cell-centered finite-volume-based perfectly matched layer for time-domain Maxwell system. IEEE Trans. Microw. Theory Tech. 54(3), 1269–1276 (2006)

    ADS  Google Scholar 

  120. W. Chew, J. Jin, Perfectly matched layers in the discretized space: an analysis and optimization. Electromagnetics 16, 325–340 (1996)

    Google Scholar 

  121. J. Fang, Z. Wu, Closed-form expression of numerical reflflection coeffificient at PML interfaces and optimization of PML performance. IEEE Microwave Guided Wave Lett. 6, 332–334 (1996)

    Google Scholar 

  122. F. Collino, P.B. Monk, Optimizing the perfectly matched layer. Comput. Methods Appl. Mech. Eng. 164, 157–171 (1998)

    ADS  MathSciNet  Google Scholar 

  123. S.C. Winton, C.M. Rappaport, Specifying PML conductivities by considering numerical reflflection dependencies. IEEE Trans. Antennas Propag. 48, 1055–1063 (2000)

    ADS  Google Scholar 

  124. X. Travassos, S. Avila, D. Prescott, A. Nicolas, L. Krahenbuhl, Optimal confifigurations for perfectly matched layers in FDTD simulations. IEEE Trans. Magnetics 42, 563–566 (2006)

    ADS  Google Scholar 

  125. A. Bermúdez, L. Hervella-Nieto, A. Prieto, R. Rodrı et al., An optimal perfectly matched layer with unbounded absorbing function for time-harmonic acoustic scattering problems. J. Comput. Phys. 223, 469–488 (2007)

    ADS  MathSciNet  Google Scholar 

  126. E. Bécache, P.G. Petropoulos, S.D. Gedney, On the long-time behavior of unsplit perfectly matched layers. IEEE Trans. Antennas Propag. 52, 1335–1342 (2004)

    ADS  MathSciNet  Google Scholar 

  127. S. Asvadurov, V. Druskin, M.N. Guddati, L. Knizhnerman, On optimal fifinite-difference approximation of PML. SIAM J. Numer. Anal. 41, 287–305 (2003)

    MathSciNet  Google Scholar 

  128. Z. Chen, H. Wu, An adaptive fifinite element method with perfectly matched absorbing layers for the wave scattering by periodic structures. SIAM J. Numer. Anal. 41, 799–826 (2003)

    MathSciNet  Google Scholar 

  129. T. Hagstrom, D. Givoli, D. Rabinovich, J. Bielak, The double absorbing boundary method. J. Comput. Phys. 259, 220–241 (2014)

    ADS  MathSciNet  Google Scholar 

  130. S. Yan, J.M. Jin, A self-dual integral equation for solving em scattering from PEC, PMC, and IBC objects. Paper presented at: Antennas and Propagation Society International Symposium, APSURSI, (Orlando, FL, 2013)

  131. V. Druskin, R. Remis, A Krylov stability-corrected coordinate-stretching method to simulate wave propagation in unbounded domains. SIAM J. Sci. Comput. 35, B376–B400 (2013)

    MathSciNet  Google Scholar 

  132. V. Druskin, R. Remis, M. Zaslavsky, An extended Krylov subspace model-order reduction technique to simulate wave propagation in unbounded domains. J. Comput. Phys. 272, 608–618 (2014)

    ADS  MathSciNet  Google Scholar 

  133. V. Druskin, S. Guttel, L. Knizhnerman, Near-optimal perfectly matched layers for indefifinite Helmholtz problems. SIAM Rev. 58, 90–116 (2016)

    MathSciNet  Google Scholar 

  134. J.H. Lee, J.L. Tassoulas, Absorbing boundary condition for scalar-wave propagation problems in infinite media based on a root-finding algorithm. Comput. Methods Appl. Mech. Eng. 330, 207–219 (2018)

    ADS  MathSciNet  Google Scholar 

  135. A. Chern, A Reflectionless discrete perfectly matched layer. J. Comput. Phys. 381, 91–109 (2019)

    ADS  MathSciNet  Google Scholar 

  136. F.Q. Hu, On absorbing boundary conditions for linearized Euler equations by a perfectly matched layer. J. Comput. Phys. 129, 201–219 (1996)

    ADS  MathSciNet  Google Scholar 

  137. S.D. Gedney, An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices. IEEE Trans. Antennas Propag. 44, 1630–1639 (1996)

    ADS  Google Scholar 

  138. P.G. Petropoulos, Reflflectionless sponge layers as absorbing boundary conditions for the numerical solution of Maxwell equations in rectangular, cylindrical, and spherical coordinates. SIAM J. Appl. Math. 60, 1037–1058 (2000)

    MathSciNet  Google Scholar 

  139. S. Abarbanel, D. Gottlieb, J.S. Hesthaven, Long time behavior of the perfectly matched layer equations in computational electromagnetics. J. Sci. Comput. 17, 405–422 (2002)

    MathSciNet  Google Scholar 

  140. J.A. Roden, S.D. Gedney, Convolutional PML (CPML): An effificient FDTD implementation of the CFS-PML for arbitrary media. Microwave Opt. Tech. Lett. 27, 334–338 (2000)

    Google Scholar 

  141. K.C. Meza-Fajardo, A.S. Papageorgiou, On the stability of a non-convolutional perfectly matched layer for isotropic elastic media. Soil Dyn. Earthq. Eng. 30, 68–81 (2010)

    Google Scholar 

  142. E. Bécache, S. Fauqueux, P. Joly, Stability of perfectly matched layers, group velocities and anisotropic waves. J. Comput. Phys. 188, 399–433 (2003)

    ADS  MathSciNet  Google Scholar 

  143. P.-R. Loh, A.F. Oskooi, M. Ibanescu, M. Skorobogatiy, S.G. Johnson, Fundamental relation between phase and group velocity, and application to the failure of perfectly matched layers in backward-wave structures. Phys. R. E 79, 065 (2009)

    Google Scholar 

  144. A.F. Oskooi, L. Zhang, Y. Avniel, S.G. Johnson, The failure of perfectly matched layers, and towards their redemption by adiabatic absorbers. Opt. Express 16, 11376–11392 (2008)

    ADS  Google Scholar 

  145. D. Appelö, G. Kreiss, A new absorbing layer for elastic waves. J. Comput. Phys. 215, 642–660 (2006)

    ADS  MathSciNet  Google Scholar 

  146. E. Bécache, M. Kachanovska, Stable perfectly matched layers for a class of anisotropic dispersive models. Part I: Necessary and suffificient conditions of stability. ESAIM Math. Model. Numer. Anal. 51, 2399–2434 (2017)

    MathSciNet  Google Scholar 

  147. K. Duru, J.E. Kozdon, G. Kreiss, Boundary conditions and stability of a perfectly matched layer for the elastic wave equation in first order form. J. Comput. Phys. 303, 372–395 (2015)

    ADS  MathSciNet  Google Scholar 

  148. G. Festa, E. Delavaud, J.-P. Vilotte, Interaction between surface waves and absorbing boundaries for wave propagation in geological basins: 2D numerical simulations, Geophys. Res. Lett. 32 (2005)

  149. A. Deinega, I. Valuev, Long-time behavior of PML absorbing boundaries for layered periodic structures. Comput. Phys. Commun. 182, 149–151 (2011)

    ADS  Google Scholar 

  150. Z. Chen, X. Wu, Long-time stability and convergence of the uniaxial perfectly matched layer method for time-domain acoustic scattering problems. SIAM J. Numer. Anal. 50, 2632–2655 (2012)

    MathSciNet  Google Scholar 

  151. W.C. Chew, W.H. Weedon, A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. IEEE Microw Guid Wave Lett. 7(13), 599–604 (1994)

    Google Scholar 

  152. M. Kuzuoglu, R. Mittra, Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers. IEEE Microw Guid Wave Lett. 6(12), 447–449 (1996)

    Google Scholar 

  153. T. Kaufmann, K. Sankaran, C. Fumeaux, R. Vahldieck, A review of perfectly matched absorbers for the finite-volume time-domain method. Appl. Comput. Electromagn. Soc. 23(3), 184–192 (2008)

    Google Scholar 

  154. J.A. Roden, S.D. Gedney, Convolution PML (CPML): an efficient FDTD implementation of the CFS-PML for arbitrary media. Microwave Opt. Technol. Lett. 27(5), 334–339 (2000)

    Article  Google Scholar 

  155. W.C. Chew, W.H. Weedon, A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. IEEE Microwave Guid Wave Lett. 7(13), 599–604 (1994)

    Google Scholar 

  156. M. Kuzuoglu, R. Mittra, Frequency dependence of the constitutive parameters of causal perfectly matched anisotropic absorbers. IEEE Microwave Guid Wave Lett. 6(12), 447–449 (1996)

    Article  Google Scholar 

  157. S.D. Gedney, B. Zhao, An auxiliary differential equation formulation for the complex-frequency shifted PML. IEEE Trans. Antennas Propag. 58(3), 838–847 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  158. A. Taflove, A perspective on the 40-year history of FDTD Computational electromagnetics. ACES J. 22(1), 1–21 (2007)

    Google Scholar 

  159. X.B. He et al., New Hybrid FDTD algorithm for electromagnetic problem analysis. Chin. Phys. B 28(7), 074102 (2019)

    Article  ADS  Google Scholar 

  160. O.M. Ramahi, V. Subramanian, B. Archambeault, A simple finite difference frequency domain(FDFD) algorithm for analysis of switching noise in printed circuit boards and packages. IEEE Trans. Adv. Packag. 26(2), 191–198 (2003)

    Article  Google Scholar 

  161. F. Xu, Y. Zhang, W. Hong, K. Wu, T.J. Cui, Finite difference frequency domain algorithm for modeling guided wave properties of substrate integrated waveguide. IEEE Trans. Microw. Theory Techniq. 51(11), 2221–2227 (2003)

    Article  ADS  Google Scholar 

  162. A. Polycarpou, B. Constantine, Introduction to the Finite Element Method in Electromagnetics (Morgan & Claypool Publisher, San Rafael, 2006)

    Book  Google Scholar 

  163. G. Meunire, The Finite Element Method for Electromagnetic Modeling (Wiley, Hoboken, 2007)

    Google Scholar 

  164. R. Li et al., Generalized Difference Methods for Differential Equations: Numerical Analysis of Finite Methods, 1st edn. (CRC Press, Boca Raton, 2000)

    Google Scholar 

  165. N.K. Madsen, R.W. Ziolkowski, A three dimensional modified finite volume technique for Maxwell’s equation. Electromagnetics 10(1-2), 147–161 (1990)

    Google Scholar 

  166. R. Holland, V.P. Cable, L.C. Wilson, finite volume time domain(FVTD) techniques for em scattering. IEEE Trans. Electromagn. Compat. 33(4), 281–294 (1991)

    Google Scholar 

  167. S. Bilbao, Modeling of complex geometries and boundary conditions in finite difference/finite volume time domain room acoustics simulation. IEEE Trans. Audio Speech Language Process. 21(7), 1524–1533 (2013)

    Google Scholar 

  168. B. He, F.L. Teixeira, Sparse and Explicit Finite Element Time Domain(FETD) Method via a Topological-based Sparsification of the Inverse Mass Matrix, Paper Presented at: Antenna and Propagation Society International Symposium, (Albuquerque, NM, 2006)

  169. Q. Qi, M. Chen, Z. Huang, X. Cao, A fast explicit FETD method based compression sensing. Prog. Electromagn. Res. 55, 161–167 (2017)

    Google Scholar 

  170. R.A. Lemdiasov, A.A. Obi, R. Ludwig, Time domain formulation of the method of moments for in-homogeneous conductive bodies at low frequencies. IEEE Trans. Antennas Propag. 54(2), 706–714 (2006)

    Article  ADS  Google Scholar 

  171. E.K. Miller, A selective survey of computational electromagnetics. IEEE Trans. Antennas Propag. 36, 1281–1305 (1988)

    Article  ADS  Google Scholar 

  172. E.K. Miller et al., Computational Electromagnetics—Frequency Domain Method of Moments (IEEE Press, Newyork, 1991)

    Google Scholar 

  173. P.B. Johns, R.L. Beurle, Numerical solutions of 2-dimensional scattering problems using a transmission line matrix. Proc. IEEE 118(9), 1203–1208 (1971)

    Google Scholar 

  174. J.R.W. Hoefer, The Transmission Line Matrix(TLM) Method Numerical Techniques for Microwave and Millimeter Wave Passive Structures (Wiley, New York, 1989), pp. 451–496

    Google Scholar 

  175. M. Krumpholz, P. Russer, A field theoretical derivation of TLM. IEEE Trans. Microwave Theory Technique 42(9), 1660–1668 (1994)

    ADS  Google Scholar 

  176. C. Christopoulos, The Transmission Line Modeling Method:TLM, Piscataway (IEEE Press, New Jersey, 1995)

    Google Scholar 

  177. T. Weiland, A discretization method for the solution of maxwell’s equations for six component fields. Electron. Commun. 31(3), 116–120 (1977)

    Google Scholar 

  178. T. Weiland, Time domain electromagnetic field computation with finite difference methods. Int. J. Numer. Model. Electronic Netw. Dev. Fields 3(3), 295–319 (1996)

    Google Scholar 

  179. J.S. Hesthaven, T. Warburton, Nodal Discontinuos Galerkin Methods: Algorithms, Analysis, and Appklications, 1st edn. (Springer, New York, 2007)

    Google Scholar 

  180. B. Cockburn et al., Discontinuous Galerkin Methods: Theory, Computation and Applications (Springer, Berlin, 2000)

    Google Scholar 

  181. H. Luo et al., A reconstructed discontinuous galerkin method for the Euler equations on arbitrary grids. Commun. Computat. Phys. 12(5), 1495–1519 (2012)

    ADS  MathSciNet  Google Scholar 

  182. H. Chen et al., A hybridizable discontinuous galerkin method for the helmholtz equation with high wave number. SIAM J. Numer. Anal. 51(4), 2166–2188 (2013)

    MathSciNet  Google Scholar 

  183. C.W. Shu, Discontinuous galerkin method for time dependent problems: survey and recent developments, in Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations The IMA Volumes in Mathematics and its Applications, vol. 157, ed. by X. Feng, et al. (Springer, Cham, 2014)

    Google Scholar 

  184. A.J. Angulo et al., 3-D Discontinuous Galerkin Time Domain Method for Anisotropic Materials. IEEE Antennas Wireless Propag. Lett. 11, 1182–1185 (2010)

    ADS  Google Scholar 

  185. D. Jugieu et al., Design and simulation of printed windin g inductors for inductive wireless power charging applications. in 2015 IEEE Wireless Power Transfer Conference(WPTC), European Union, (2015), pp. 1–4

  186. K. Sharma, R. Mittra, Novel technique for numerical efficient solution of multiscale problems in computational electromagnetic. Int. J. Numer. 57(7), 2094–2104 (2009)

    Google Scholar 

  187. C.J. Reddy, Analysis of airborne antennas using hybrid computational techniques. in 2018 IEEE International Symposium on Antenna and Propagation & USNC/URSI National Radio Science Meeting, pp. 1229–1230

  188. Branin Jr., F.H, Problem Analysis in Science and Engineering.In: The Network Concept as a Unifying Principle in Engineering and the Physical Sciences, Academic Press, pp.41-111, 1977

  189. E. Tonti, Finite Formulation of the EM field. Prog. Electromagn. Res. 32, 1–44 (2001)

    Google Scholar 

  190. K. SankaraN, D.I.V. Beyond, CURL and grad: modeling EM problems using algebraic topology. J. Electromagn. Waves Appl. 31, 121–149 (2017)

    Google Scholar 

  191. J.F. Lee, R. Lee, A. Cangellaris, Time domain finite element methods. IEEE Trans. Antennas Propag. 45(3), 430–442 (1997)

    ADS  MathSciNet  Google Scholar 

  192. T.V. Yioultsis, N.V. Kantartzis, C.S. Antonopoulos, T.D. Tisboukis, A fully explicit whitney element time domain scheme with higher order vector finite elements for three dimensional high frequency problems. IEEE Trans. Mag. 34(5), 3288–3291 (1998)

    ADS  Google Scholar 

  193. J. Velasco et al., Finite element modeling of thin conductors in frequency domain. IEEE Trans. Mag. (2019). https://doi.org/10.1109/tmag.2019.2955514

    Article  Google Scholar 

  194. U.Gavrilieva et al., Generalized Multi-scale Finite Element Method for Elastic Wave Propagation in Frequency Domain, Computation, vol. 83, no. 3, (2020)

  195. H. Liu et al., Simulation of ground penetration radar on dispersive media by a finite element time domain algorithm. J. Appl. Geophys. (2019). https://doi.org/10.1016/j.jappgeo.2019.103821

    Article  Google Scholar 

  196. J.M. Jin, The Finite Element Method in Electromagnetics (Wiley, Hoboken, 2015)

    Google Scholar 

  197. J. Li et al., A finite element time domain forward solver for electromagnetic methods with complex shaped loop sources. Geophysics 83(3), 117–132 (2018)

    Google Scholar 

  198. D. Jiao, J.M. Jin, A general approach for the stability analysis of time domain finite element method for electromagnetic simulations. IEEE Trans. Antenna Simul. 50(11), 1624–1632 (2002)

    ADS  Google Scholar 

  199. K.Tagger et al., High Order and Unconditionally Stable Time Domain Finite Element Method, IEEE Antenna and Wireless Propagation Letters, pp.1–5, 2019, https://doi.org/10.1109/lawp.2019.2929734

  200. Y. Srikuch, Development of Hybrid Explicit/Implicit and Adaptive h and p Refinement for Finite Element Time Domain Method, Ph.D. Dissertation, (Electrical and Computer Engineering Department, Ohio State University, Columbus, OH, 2005)

  201. J. Jin, The Finite Element Method in Electromagnetics, 2nd edn. (Wiley, Hoboken, 2002), pp. 534–829

    Google Scholar 

  202. E.U. Schankee, Three Dimensional Finite Element Time Domain Modeling of the Marine Controlled Source Electromagnetic Method, Ph.D. Dissertation, (Department of Geophysics, Standford University, 2011)

  203. X. Lu et al., Wideband low frequency design of inductors and wireless power transfer coils using the mixed finite element time domain. IEEE Microwave Wireless Components Lett. 30(7), 709–712 (2020)

    Google Scholar 

  204. L. Li et al., Auxiliary differential equation finite element time domain method for electromagnetic analsis of dispersive media. Optik 184, 189–196 (2019)

    ADS  Google Scholar 

  205. Z. Zhang et al., Non-split PML boundary condition for finite element time domain modeling of ground penetrating radar. J. Appl. Math. Phys. 7(5), 1077–1096 (2019)

    Google Scholar 

  206. M. Costabel, F.J. Sayas, Time Dependent Problems with the Boundary Integral Equation Method, Encyclopedia of Computational Mechanics, 2nd Edition, https://doi.org/10.1002/97811191/76817.ecm2022

  207. A. Dedner, D. Kroner, C. Rhode, T. Schnitzer, M. Wesenberg, Comparison of high-order finite volume and discontinuous galerkin methods of higher order for systems of conservation laws in multiple space dimensions. in Geometric Analysis and Non-linear Partial Differential Equations, (Springer, Berlin, 2003), pp. 573–589

  208. A.F. Antoniadis, K.H. Iqbal, E. Shapiro, N. Asproulis, D. Drikakis, Comparison of high-order finite volume and discontinuous galerkin methods on 3d unstructured grids, in AIP Conference Proceedings, vol. 1389, ed. by T.E. Simos, C. Psihoyios, Z. Anastassi (Melville, NY, 2011)

    Google Scholar 

  209. A.B. Aakash, K. Sankaran, Tumour Electrotherapy Modelling Using Algebraic Topological Method, Paper Presented At: 2019 Ursi Asia- Pacific Radio Science Conference(Ap-Rasc) (New Delhi, India, 2019)

    Google Scholar 

  210. A.B. Aakash, K. Sankaran, Algebraic Topological Method: An Alternative Modelling Tool for Electromagnetics, Paper Presented at: 2019 URSI Asia-Pacific Radio Science Conference(AP-RASC) (New Delhi, India, 2019)

    Google Scholar 

  211. E.K. Miller, A selective survey of computational electromagnetics. IEEE Trans. Antenna Propag. 36, 1281–1305 (1988)

    ADS  Google Scholar 

  212. E.K. Miller et al., Computational electromagnetics - frequency domain method of moments (IEEE Press, New York, 1991)

    Google Scholar 

  213. W.D. Murphy et al., Acceleration methods for the iterative solution of EM scattering problems. Radio Sci. 28, 1–12 (1993)

    ADS  Google Scholar 

  214. E. Garcia, Computational Electromagnetics: Recent Advances and Engineering Applications, 1st edn. (Springer, New York, 2014)

    Google Scholar 

  215. I. Daubechies, Ten Lectures on Wavelets CBMS-NSF Series in Applied Mathematics (SIAM, Philadelphia, 1992)

    Google Scholar 

  216. T.K. Sarkar et al., Survey of numerical methods for solutions of large systems of linear equations for electromagnetic field problems. IEEE Trans. Antennas Propag. 29, 847–856 (1981)

    ADS  MathSciNet  Google Scholar 

  217. K. Kalbasi, D.R. Demarest, A multilevel formulation of the method of moments. IEEE Trans. Antennas Propag. 41, 589–599 (1993)

    ADS  Google Scholar 

  218. R. Coifman et al., The fast multipole method for the wave equation: a pedestrian prescription. IEEE Trans. Antennas Propag. 35, 7–12 (1993)

    MathSciNet  Google Scholar 

  219. W.C. Chew et al., A generalized recursive algorithm for wave-scattering solutions in two dimensions. IEEE Trans. Microwave Theory Techniques 40, 716–723 (1992)

    ADS  Google Scholar 

  220. W.C. Chew et al., A recursive algorithm for wave scattering using windowed addition theorem. J. Electromagn. Waves Appl. 6(7), 1537–1560 (1992)

    Google Scholar 

  221. W.C. Chew, C.C. Lu, NEPAL- an algorithm for solving the volume integral equation. Microwave Opt. Technol. Lett. 6, 185–188 (1993)

    ADS  Google Scholar 

  222. K.R. Umashanker et al., Numerical analysis of electromagnetic scattering by electrically large objects using spatial decomposition technique. IEEE Trans. Antennas Propag. 40, 867–877 (1992)

    ADS  Google Scholar 

  223. F.X. Canning, The Impedance matrix localization method for moment calculations. IEEE Trans. Antennas Propag. 32, 18–30 (1990)

    Google Scholar 

  224. F.X. Canning, Improved impedance matrix localization method. IEEE Trans. Antennas Propag. 41, 659–667 (1993)

    ADS  Google Scholar 

  225. Y. Leviatan, A. Boag, Analaysis of electromagnetic from dielectric cylinders using a multi-filament current model. IEEE Trans. Antennas Propag. 35, 1119–1127 (1987)

    ADS  Google Scholar 

  226. Y. Leviatan et al., A method of moments analysis of electromagnetic coupling through slots using Gaussian beam expansions. IEEE Trans. Antennas Propag. 37, 1537–1544 (1989)

    ADS  Google Scholar 

  227. A.C. Ludwig, A new technique for numerical electromagnetic. IEEE Trans. Antennas Propag. 37, 40–41 (1989)

    Google Scholar 

  228. C. Hafner, The Generalized Multipole Technique (Artech, Boston, 1990)

    Google Scholar 

  229. C. Hafner, On the relationship between MOM and GMT. IEEE Trans. Antennas Propag. 34, 12–19 (1990)

    Google Scholar 

  230. F.P. Andriulli et al., A marching on-in-time hierarchical scheme for the solution of time domain electrical field integral equation. IEEE Trans. Antennas Propag. 55(12), 3734–3738 (2007)

    ADS  MathSciNet  Google Scholar 

  231. G. Manara, A. Monorchio, R. Reggiannini, A space-time discretization creteria for a stable time marching solution of the electric field integral equation. IEEE Trans. Antennas Propag. 45(3), 527–532 (1997)

    ADS  Google Scholar 

  232. J. Kornprobst, T.F. Eibert, Investigations on the solution of the magnetic field integral equation with Rao-Wilton-Glisson basis function. in 2019 International Conference on Electromagnetics in Advanced Applications(ICEAA), (Granada, Spain, 2019)

  233. M. Bertrand et al., RWG basis functions for accurate modeling of substrate integtrated waveguide slot-based antennas. Trans. Magn. 56(1), 1–4 (2020)

    Google Scholar 

  234. M. Tanaka, K. Tanaka, Magnetic field integral equation for three dimensional hollow waveguide. in 2017 IEEE International Conference on Computational Electromagnetics(ICCEM), (2017), pp. 284–285

  235. R.L. Barbosa, F.J. da Silva Moreira, Propagation prediction based on time domain electric field integral equation for smoothly irregular terrains. in 12th European Conference on Antennas and Propagation(EuCAP2018), (2018), pp. 1–18

  236. H.A. Ulku et al., Marching-on-in-time(MOT) solution of the time domain magnetic field integral equation using a predictor-collector scheme. IEEE Trans. Antennas Propag. 61(8), 4120–4131 (2013)

    ADS  Google Scholar 

  237. Y.T. Wu, W.-X. Sheng, Analysis of initial condition problem and linear loop modes in the solution of the derivative form of time domain electric field integral equation. IEEE Antennas Wireless Propag. Lett. 18(4), 636–640 (2019)

    ADS  Google Scholar 

  238. M.D. Zhu et al., On the stability of time-domain-magnetic-field integral equation using laguerre functions. IEEE Trans. Antennas Propag. 67(6), 3939–3947 (2019)

    ADS  Google Scholar 

  239. Z. Ye, X. Liao, J. Zhang, A novel three dimensional FDTD sub-gridding method for the coupling analysis of shielded cavity by ambient wave. IEEE Trans. Electromagn. Compat. (2019). https://doi.org/10.1109/temc.2019.2955445

    Article  Google Scholar 

  240. B.M. Kolundzija et al., From low to ultra high order basis functions: general approach for highly accurate and efficient electromagnetic modeling. in 2019 International Conference on Electromagnetic in Advanced Applicatiobns(ICEAA), (2019). https://doi.org/10.1109/iceaa.2019.8879043

  241. K. Sharma, R. Mittra, Novel techniques for numerically efficient solution of multi-scale problems in computational electromagnetic. Int. J. Numer. Model. vol. 33, no. 2, (2020)

  242. K.S. Yee, J.S. Chen, The finite difference time domain(FDTD) and the finite volume time domain(FVTD) methods in solving Maxwell’s equations. IEEE Trans. Antenna Propag. 45(3), 354–363 (1997)

    ADS  Google Scholar 

  243. M. El Hachemi et al., Hybrid methods for electromagnetic scattering simulations on over-lapping grids. Commun. Numer. Methods Eng. 19, 749–760 (2003)

    Google Scholar 

  244. A. Monorchio et al., A hybrid time domain technique that combines the FE, FD and MOM techniques to solve complex electromagnetic problems. IEEE Trans. Antennas Propag. 52(10), 2666–2674 (2004)

    ADS  MathSciNet  Google Scholar 

  245. L. Sevgi, EMC and BEM engineering education: physics-based modeling, hands-on training, and challenges. IEEE Antennas Propag. Mag. 45(2), 114–119 (2003)

    ADS  Google Scholar 

  246. L.B. Felsen, L. Sevgi, Electromagnetic engineering in the 21st century: challenges and perspectives. Turkish J. Electrical Eng. 10(2), 132–145 (2002)

    Google Scholar 

  247. H.E. Taylor et al., Discussion of a physical optics method and its application to absorbing smooth and slightly rough hexagonal prisms. J. Quantitat. Spectrosc. Radiat. Transfer 218, 54–67 (2018)

    ADS  Google Scholar 

  248. R. Zhang et al. Designing a radome with frequency selective surface by using physical optics method. in 2016 11th International Symposium on Antennas, Propagation and Electromagnetic Theory(ISAPE), 2016

  249. D. Klemant et al., Special problems in applying the physical optics method for backscatterer computations of complicated objects. IEEE Trans. Antenna Propag. 36(2), 228–237 (1988)

    ADS  Google Scholar 

  250. J. Chungang et al., Time domain physical optics method for the analysis of wideband electromagnetic scattering from two dimensional conducting rough surface. vol. 2013, pp. 1–9, (2013)

  251. P.Y. Ufimtsev, Fundamentals of the physical theory of diffraction. IEEE Antennas Propag. Mag. 50(1), 159–161 (2008)

    Google Scholar 

  252. N.N. Gorobets et al., Directivity characteristics research of scanning and multibeam reflector antennas by the current method of physical diffraction theory. in 2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and submillimeter waves(MSMW), (2016), pp.1–3

  253. P.Y. Ufimtsev, Fundamentals of the physical theory of diffraction, 2nd edn. (Wiley, Hoboken, 2014)

    Google Scholar 

  254. C. Balanis, L. Sevgi, P.Y. Ufimtsev, Fifty years of high frequency asymptotics. Int. J. RF Microw. Comput. Aid. Eng. 23(4), 394–402 (2013)

    Google Scholar 

  255. P.Y. Ufimtsev, Fundamentals of the Physical Theory of Diffraction (Wiley, New York, 2007)

    Google Scholar 

  256. P.Y. Ufimtsev, Elementary edge waves and the physical theory of diffraction. Electromagnetics 11(2), 125–160 (1991)

    Google Scholar 

  257. P.Y. Ufimtsev, Theory of Edge Diffraction in Electromagnetics: Origination and Validation of the Physical Theory of Diffraction (SciTech Publishing Inc, Raleigh, 2009)

    Google Scholar 

  258. A. Rubinowicz, Zur kirchhoffschen beugungstheorie. Ann. Phys. 73(4), 339–364 (1924)

    Google Scholar 

  259. P.Y. Ufimtsev, Rubinowicz and Theory of Edge Waves. Microwave Conference, vol. 2 (Zakopane, Poland, 1983)

    Google Scholar 

  260. P.Y. Ufimtsev, Rubinowicz and the modern theory of diffracted rays. Electromagnetics 15(5), 547–565 (1995)

    Google Scholar 

  261. R.A. Shore, A.D. Yaggjian, Incremental diffraction coefficients for planar surfaces. IEEE Trans. Antennas Propag. 36(1), 55–70 (1998)

    ADS  Google Scholar 

  262. A.D. Yaghjian, R.A. Shore, M.B. Woodworth, Shadow boundary incremental length diffraction coefficients for perfectly conducting smooth, convex surfaces. Radio Sci. 31(6), 1681–1695 (1996)

    ADS  Google Scholar 

  263. D. Erricolo et al., Experimental and theoretical validation for the incremental theory of diffraction. IEEE Trans. Antennas Propag. 56(8), 2563–2571 (2008)

    ADS  Google Scholar 

  264. A.A. Fuki, Geometrical Optics of Weakly Anisotropic Media, 1st edn. (Routledge, London, 1998)

    Google Scholar 

  265. A.D. Simone et al., Analytical modeld for the electromagnetic scattering from isolated targets in bistatic configuration: geometrical optics solution. IEEE Trans. 58(2), 861–880 (2019)

    Google Scholar 

  266. S. Jin, D. Yin, Computational high frequency wave diffraction by a corner via the liouville equation and geometry theory of diffraction. Kinetic & Related Models 4(1), 295–316 (2011)

    MathSciNet  Google Scholar 

  267. A. Ishimaru, Electromagnetic wave propagation, radiation scattering: from fundamentals to applications, 2nd Edition. in The Institute of Electrical and Electronics Engineers, (Wiley, 2017)

  268. D. Tami et al., Analysis of Heuristic uniform theory of diffraction co-efficients for electromagnetic scattring prediction. Int. J. Antenna Propag. 1, 1–11 (2018)

    Google Scholar 

  269. S. Chehade et al., The spectral functions method for ultrasonic plane wave diffraction by a soft wedge. J. Phys. Conf. Ser. vol. 1184, no.1, (2019)

  270. Y.Z. Umal, Uniform Asymptotic Theory for the Edge Diffraction of Cylindrical waves. IET Microw. Antennas Propag. 11(15), 2219–2222 (2017)

    Google Scholar 

  271. D. Kandimalla, A. De, High Frequency Uniform Asymptotic Solution for Diffraction by the Edges of a Cueved Plate, (IEEE, 2018)

  272. H.E. Taylor et al., Discussion of a physical optics method and its application to absorbing smooth and slightly rough hexagonal prisms. J. Quantitat. Spectrosc. Radiat. Trans. 218, 54–67 (2018)

    ADS  Google Scholar 

  273. R. Zhang et al., Designing a radome with frequency selective surface by using physical optics method. in 2016 11th International Symposium on Antennas, Propagation and Electromagnetic Theory(ISAPE), (2016)

  274. J. Chungang et al., Time Domain Physical Optics Method for the Analysis of Wideband Electromagnetic Scattering from Two Dimensional Conducting Rough Surface, (2013), vol. 2013, pp. 1–9

  275. J. Perez, M.F. Catedra, Applications of physical optics to the rcs computation of bodies modeled with NURBS surfaces. IEEE Trans. Antenna Propag. 42(10), 1404–1411 (1994)

    Article  ADS  Google Scholar 

  276. M. Potgieter, Bistatic RCS calculations of complex realistic targets using asymptotic methods. in Proceeding of 2018 International Workshop on Computing, Electromagnetic and Machine Intelligence(CEMi), (2018), pp. 23–24

  277. M. Shafieipour et al., On error controlled computing of the near electromagnetic fields in the shade regions of electrically lrge 3D objects. in Proceedings 2016 URSI International Symposium Electromagnetic Theory(EMTS), (2016), pp. 203–206

  278. R. Ross, Radar cross-section of rectangular flat plates as a function of aspect angle. IEEE Trans. Antenna Propag. 14(3), 329–335 (1966)

    Article  ADS  Google Scholar 

  279. T. Pairon et al., Improved physical optics (IPO) computing near the near forward scattering region: application to 2D scenarios. IEEE Trans. Antenna Propag. (2020). https://doi.org/10.1109/tap.2020.3008669

    Article  Google Scholar 

  280. B. Chen, C. Tong, Modified physical optics algorithm for near field scattering. Chin. Phys. B 27(11), 114102 (2018)

    Article  ADS  Google Scholar 

  281. P.Y. Ufimtsev, GTD as the asymptotic form of the method of edge waves. in Digests of the 7th All-Union Symposium on Diffraction and Propagation, Rostov-on Don, (1977), pp. 54–57

  282. P.Y. Ufimtsev, Theory of acoustical edge waves. J. Acoust. Soc. Am. 86(2), 463–474 (1989)

    Article  ADS  Google Scholar 

  283. P.Y. Ufimtsev, Improved physical theory of diffraction: removal of grazing singularity. IEEE Trans. Antennas Propag. 54(10), 2698–2702 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  284. P.Y. Ufimtsev, The 50 year anniversary of the PTD; comments on the PTD’s origin and development. IEEE Antennas Propag. Mag. 55(3), 18–28 (2013)

    Article  ADS  Google Scholar 

  285. H. Kobayashi et al., Scattering of plane wave by a 3D smooth convex impedance surface using PTD with transition currents. Electron. Commun. Jpn. 85(2), 1325–1334 (2002)

    Google Scholar 

  286. P. Usai et al., RCS calculation and validation through measuremwents of electrically large objects partially covered with thin radar absorbing metamaterials. in 2019 International Conference on Electromagnetics in Advanced Applications(ICEAA), (2019)

  287. V.A. Akhiyrov et al., Mathematical modeling of EM scattering field from perfectly conducting object with dielectric cover on the base of physical theory of diffraction. in 12th European Conference on Antennas and Propagation(EUCAP2018)

  288. N.N. Gorobets et al., Directivity characteristics research of scanning and multibeam reflector antennas by the current method of physical diffraction theory. in 2016 9th International Kharkiv Symposium on Physics and Engineering of Microwaves, Millimeter and submillimeter waves(MSMW), (2016), pp. 1–3

  289. G. Pelosi, Y. Rahmat-Samii, J. Volakis, High-frequency techniques in diffraction theory: 50 years of achievements in GTD, PTD, and related approaches. IEEE Antennas Propag. Mag. 55(3), 16–17 (2013)

    Article  ADS  Google Scholar 

  290. A. Ishimaru, Electromagnetic wave propagation, radiation scattering:from fundamentals to applications. in 2nd Edition, In: The Institute of Electrical and Electronics Engineers, (Wiley, 2017)

  291. Y.Z. Umul, Improved equivalent source theory. J. Opt. Soc. Am. 26, 1798–1804 (2009)

    Article  ADS  Google Scholar 

  292. Y.Z. Umul, Modified theory of physical optics and the correction terms of the physical theory of diffraction. Opt. Int. J. Light Electron Opt. vol. 171, (2018)

  293. Y.Z. Umul, Three dimensional modified theory of physical optics. Opt. Int. J. Light Electron Opt. 127, 819–824 (2016)

    Article  Google Scholar 

  294. Z. Cao et al., Geometrical optics approximation for plane wave scattering by a rectangular groove on a surface. Appl. Opt. 59(8), 2600–2605 (2020)

    Article  ADS  Google Scholar 

  295. A.R. Assis, GO synthesis of offset dual reflector antennas using local axis displaced confocal quadrics. J. Microw. Optielectron. Electromagn. Appl. 19(2), 177–190 (2020)

    Article  Google Scholar 

  296. N. Lopez, I. Dodin, Restoring Geometrical Optics Near Caustics Using Sequenced Metaplectic Transform, (2020). arxiv:20004.10639

  297. L.S. Aslanyan, H.H. Hovakim, Geometrical optics of an anisotropic media with space modulated gyrotropy. J. Contemp. Phys. 55, 30–37 (2020)

    Google Scholar 

  298. M. Safak, Calculation of radiation patterns of paraboloidal reflectors by high frequency asymptotic techniques. Electron. Lett. 12(6), 229 (1976). https://doi.org/10.1049/el.19760176

    Article  ADS  Google Scholar 

  299. G. Ahmed, S.A. Mohsin, High frequency techniques for reflector antenna analysis. in 2009 Third International Conference on Electrical Engineering. https://doi.org/10.1109/icee2009.5173181

  300. X. Zhang et al., GTD including corner diffractions with application to radiation pattern analysis of major angle corner reflector antenna. Electron. Commun. Jpn. 74(11), 11–22 (1991). https://doi.org/10.1002/ecjb.4420741102

    Article  Google Scholar 

  301. H. Kobayashi et al., Radar imaging by using GTD Near-field model and antenna array factor. in 2012 Internatioal Symposium on Antenna and Propagation(ISAP), (2012), pp. 616–619

  302. R.G. Konyoumjian, P.H. Pathak, A uniform geometrical theory of diffraction for an edge in a perfectly conducting surface. Proc. IEEE 62(11), 1448–1461 (1974)

    ADS  Google Scholar 

  303. R. Corriere et al., Radar target modeling: a geometric theory of diffraction (GTD) based approach. Proc. SPIE (1994). https://doi.org/10.1117/12.181041

    Article  Google Scholar 

  304. S. Jin, D. Yin, Computational high frequency wave diffraction by a corner via the liouville equation and geometry theory of diffraction. Kinetic Relat. Models 4(1), 295–316 (2011)

    MathSciNet  Google Scholar 

  305. M. Ali, S. Sanyal, A finite edge GTD analysis of the h-plane horn radiation pattern. IEEE Trans. Antenna Propagat. 58(3), 969–973 (2010)

    ADS  Google Scholar 

  306. V.M. Babic, N.Y. Kirpivnikova, The Boundary Layer Method in Diffraction Problems, 1st edn. (Springer, Berlin, 1979)

    Google Scholar 

  307. Y. Rahmat-Samii, GTD, UTD, UAT and STD: a historical revisit and personal observations. IEEE Antennas Propagat. Mag. 55(3), 29–40 (2013)

    ADS  Google Scholar 

  308. M. Balasubramanian et al., A heuristic UTD solution for scattering by a thin lossless anisotropic slab. IEEE Trans. Antenna Propagat. (2020). https://doi.org/10.1109/tap.2020.3001425

    Article  Google Scholar 

  309. K. Phaebua et al., Path-loss prediction of radio wave propagation on an orchard by using modified UTD method. PIER Prog. Electromagn. Res. 128, 347–363 (2012)

    Google Scholar 

  310. G.S. Rosa, F.J.V. Hasselmann, A high frequency uniform asymptotic solution for electromagnetic field scattering by a PEC wedge including grazing incidence and propagation. IEEE Trans. Antenna Propagat. (2020). https://doi.org/10.1109/tap.2020.2987415

    Article  Google Scholar 

  311. M.H. Shahzad et al., High frequency energy distribution of a plasma coated paraboloid reflector. Prog. Electromagn. Res. 92, 11–20 (2020). https://doi.org/10.2528/pierm20022403

    Article  Google Scholar 

  312. B.F. Molinet, R. Mittra, Asymptotic Methods in Electromagnetics (Springer, Berlin, 2012)

    Google Scholar 

  313. E. Torabi et al., Modification of the UTD model for cellular mobile communication in an urban environment. Electromagnetics 27(5), 263–285 (2007)

    Google Scholar 

  314. F. Weinmann, Ray tracing with PO/PTD for RCS modeling of large complex objects. IEEE Trans. Antennas Propagat. 54(6), 1797–1806 (2006)

    ADS  Google Scholar 

  315. A. Barka, N. Douchin, Asymptotic simplifications for hybrid BEM/GO/PO/PTD techniques based on a generalized scattering matrix approach. Comput. Phys. Commun. 183(9), 1928–1936 (2012)

    ADS  MathSciNet  Google Scholar 

  316. A. Fedeli, M. Pastorino, A. Randazzo, A hybrid asymptotic-FVTD method for the estimation of the radar cross section of 3D structures. Electronics 8, 1–10 (2019)

    Google Scholar 

  317. D.J. Riley et al., Electromagnetic coupling and interference predictions using the frequency-domain physical optics method and the FETD method. in IEEE Antennas and Propagation Society Symposium, (2004)

  318. A. Nog, T. Topa, D. Wojcik, Analysis of complex radiating structures of Hybrid FDTD-MOM-PO method. PIERS Online 5(8), 711–715 (2009)

    Google Scholar 

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  1. Mekelle University Ethiopian Institute of Technology, Mek’ele, Ethiopia

    Mohammed Ismail Mohammed, Mahder Girmay Gebremicaheal & Gebremichael Yohannes

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Mohammed, M.I., Gebremicaheal, M.G. & Yohannes, G. CEM methods in R.F and microwave engineering in the context of parameters that influence the outcome of modeling. Eur. Phys. J. Plus 135, 829 (2020). https://doi.org/10.1140/epjp/s13360-020-00854-2

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