Skip to main content
SpringerLink
Log in

Systems of Differential Algebraic Equations in Computational Electromagnetics

  • Chapter
  • First Online:
Applications of Differential-Algebraic Equations: Examples and Benchmarks

Part of the book series: Differential-Algebraic Equations Forum ((DAEF))

Abstract

Starting from space-discretisation of Maxwell’s equations, various classical formulations are proposed for the simulation of electromagnetic fields. They differ in the phenomena considered as well as in the variables chosen for discretisation. This contribution presents a literature survey of the most common approximations and formulations with a focus on their structural properties. The differential-algebraic character is discussed and quantified by the differential index concept.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Albanese, R., Coccorese, E., Martone, R., Miano, G., Rubinacci, G.: On the numerical solution of the nonlinear three-dimensional eddy current problem. IEEE Trans. Magn. 27(5), 3990–3995 (1991). https://doi.org/10.1109/20.104976

    Article  Google Scholar 

  2. Alonso Rodríguez, A., Raffetto, M.: Unique solvability for electromagnetic boundary value problems in the presence of partly lossy inhomogeneous anisotropic media and mixed boundary conditions. Math. Models Methods Appl. Sci. 13(04), 597–611 (2003). https://doi.org/10.1142/S0218202503002672

    Article  MathSciNet  MATH  Google Scholar 

  3. Alonso Rodríguez, A., Valli, A.: Eddy Current Approximation of Maxwell Equations. Modeling, Simulation and Applications, vol. 4. Springer, Heidelberg (2010). https://doi.org/10.1007/978-88-470-1506-7

    Book  MATH  Google Scholar 

  4. Alotto, P., De Cian, A., Molinari, G.: A time-domain 3-D full-Maxwell solver based on the cell method. IEEE Trans. Magn. 42(4), 799–802 (2006). https://doi.org/10.1109/tmag.2006.871381

    Article  Google Scholar 

  5. Assous, F., Ciarlet, P., Labrunie, S.: Mathematical Foundations of Computational Electromagnetism. Springer, Cham (2018)

    Book  MATH  Google Scholar 

  6. Außerhofer, S., Bíró, O., Preis, K.: Discontinuous Galerkin finite elements in time domain eddy-current problems. IEEE Trans. Magn. 45(3), 1300–1303 (2009)

    Article  MATH  Google Scholar 

  7. Bartel, A., Baumanns, S., Schöps, S.: Structural analysis of electrical circuits including magnetoquasistatic devices. Appl. Numer. Math. 61, 1257–1270 (2011). https://doi.org/10.1016/j.apnum.2011.08.004

    Article  MathSciNet  MATH  Google Scholar 

  8. Baumanns, S.: Coupled electromagnetic field/circuit simulation: modeling and numerical analysis. Ph.D. thesis, Universität zu Köln, Köln (2012)

    Google Scholar 

  9. Baumanns, S., Selva Soto, M., Tischendorf, C.: Consistent initialization for coupled circuit-device simulation. In: Roos, J., Costa, L.R.J. (eds.) Scientific Computing in Electrical Engineering SCEE 2008. Mathematics in Industry, vol. 14, pp. 297–304. Springer, Berlin (2010). https://doi.org/10.1007/978-3-642-12294-1_38

    Chapter  Google Scholar 

  10. Baumanns, S., Clemens, M., Schöps, S.: Structural aspects of regularized full Maxwell electrodynamic potential formulations using FIT. In: Manara, G. (ed.) Proceedings of 2013 URSI International Symposium on Electromagnetic Theory (EMTS), pp. 1007–1010. IEEE, New York (2013)

    Google Scholar 

  11. Becks, T., Wolff, I.: Analysis of 3-d metallization structures by a full-wave spectral-domain technique. IEEE Trans. Microwave Theory Tech. 40(12), 2219–2227 (1992). https://doi.org/10.1109/22.179883

    Article  Google Scholar 

  12. Bedrosian, G.: A new method for coupling finite element field solutions with external circuits and kinematics. IEEE Trans. Magn. 29(2), 1664–1668 (1993). https://doi.org/10.1109/20.250726

    Article  Google Scholar 

  13. Bíró, O., Preis, K.: On the use of the magnetic vector potential in the finite-element analysis of three-dimensional eddy currents. IEEE Trans. Magn. 25(4), 3145–3159 (1989). https://doi.org/10.1109/20.34388

    Article  Google Scholar 

  14. Bíró, O., Preis, K.: Finite element analysis of 3-d eddy currents. IEEE Trans. Magn. 26(2), 418–423 (1990). https://doi.org/10.1109/20.106343

    Article  MATH  Google Scholar 

  15. Bíró, O., Preis, K., Richter, K.R.: Various FEM formulations for the calculation of transient 3d eddy currents in nonlinear media. IEEE Trans. Magn. 31(3), 1307–1312 (1995). https://doi.org/10.1109/20.376269

    Article  Google Scholar 

  16. Boffi, D.: Finite element approximation of eigenvalue problems. Acta. Numer. 19, 1–120 (2010). https://doi.org/10.1017/S0962492910000012

    Article  MathSciNet  MATH  Google Scholar 

  17. Bondeson, A., Rylander, T., Ingelström, P.: Computational Electromagnetics. Texts in Applied Mathematics. Springer, Berlin (2005). https://doi.org/10.1007/b136922

  18. Bossavit, A.: Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism. IEE Proc. 135(8), 493–500 (1988). https://doi.org/10.1049/ip-a-1:19880077

    Google Scholar 

  19. Bossavit, A.: Differential geometry for the student of numerical methods in electromagnetism. Technical Report, Électricité de France (1991)

    Google Scholar 

  20. Bossavit, A.: Computational Electromagnetism: Variational Formulations, Complementarity, Edge Elements. Academic Press, San Diego (1998)

    MATH  Google Scholar 

  21. Bossavit, A.: On the geometry of electromagnetism. (4): ‘Maxwell’s house’. J. Jpn. Soc. Appl. Electromagn. Mech. 6(4), 318–326 (1999)

    Google Scholar 

  22. Bossavit, A.: Stiff problems in eddy-current theory and the regularization of Maxwell’s equations. IEEE Trans. Magn. 37(5), 3542–3545 (2001). https://doi.org/0018-9464/01<currencydollar>10.00

    Article  Google Scholar 

  23. Bossavit, A., Kettunen, L.: Yee-like schemes on a tetrahedral mesh, with diagonal lumping. Int. J. Numer. Modell. Electron. Networks Devices Fields 12(1-2), 129–142 (1999). https://doi.org/10.1002/(SICI)1099-1204(199901/04)12:1/2<129::AID-JNM327>3.0.CO;2-G

    Article  MATH  Google Scholar 

  24. Bossavit, A., Kettunen, L.: Yee-like schemes on staggered cellular grids: a synthesis between FIT and FEM approaches. IEEE Trans. Magn. 36(4), 861–867 (2000). https://doi.org/10.1109/20.877580

    Article  Google Scholar 

  25. Brenan, K.E., Campbell, S.L., Petzold, L.R.: Numerical Solution of Initial-Value Problems in Differential-Algebraic Equations. SIAM, Philadelphia (1995)

    Book  MATH  Google Scholar 

  26. Carpenter, C.J.: Comparison of alternative formulations of 3-dimensional magnetic-field and eddy-current problems at power frequencies. IEE Proc. B Electr. Power Appl. 127(5), 332 (1980). https://doi.org/10.1049/ip-b:19800045

    Article  Google Scholar 

  27. Chen, Q., Schoenmaker, W., Chen, G., Jiang, L., Wong, N.: A numerically efficient formulation for time-domain electromagnetic-semiconductor cosimulation for fast-transient systems. IEEE Trans. Comput. Aided. Des. Integrated Circ. Syst. 32(5), 802–806 (2013). https://doi.org/10.1109/TCAD.2012.2232709

    Article  Google Scholar 

  28. Clemens, M.: Large systems of equations in a discrete electromagnetism: formulations and numerical algorithms. IEE. Proc. Sci. Meas. Tech. 152(2), 50–72 (2005). https://doi.org/10.1049/ip-smt:20050849

    Article  Google Scholar 

  29. Clemens, M., Weiland, T.: Transient eddy-current calculation with the FI-method. IEEE Trans. Magn. 35(3), 1163–1166 (1999). https://doi.org/10.1109/20.767155

    Article  Google Scholar 

  30. Clemens, M., Weiland, T.: Regularization of eddy-current formulations using discrete grad-div operators. IEEE Trans. Magn. 38(2), 569–572 (2002). https://doi.org/10.1109/20.996149

    Article  Google Scholar 

  31. Clemens, M., Wilke, M., Weiland, T.: Linear-implicit time-integration schemes for error-controlled transient nonlinear magnetic field simulations. IEEE Trans. Magn. 39(3), 1175–1178 (2003). https://doi.org/10.1109/TMAG.2003.810221

    Article  Google Scholar 

  32. Clemens, M., Schöps, S., De Gersem, H., Bartel, A.: Decomposition and regularization of nonlinear anisotropic curl-curl DAEs. Int. J. Comput. Math. Electr. Electron. Eng. 30(6), 1701–1714 (2011). https://doi.org/10.1108/03321641111168039

    Article  MathSciNet  MATH  Google Scholar 

  33. Cortes Garcia, I., De Gersem, H., Schöps, S.: A structural analysis of field/circuit coupled problems based on a generalised circuit element (2018, submitted). arXiv:1801.07081

    Google Scholar 

  34. CST AG: CST STUDIO SUITE 2016 (2016). https://www.cst.com

  35. De Gersem, H., Hameyer, K.: A finite element model for foil winding simulation. IEEE Trans. Magn. 37(5), 3472–3432 (2001). https://doi.org/10.1109/20.952629

    Google Scholar 

  36. De Gersem, H., Weiland, T.: Field-circuit coupling for time-harmonic models discretized by the finite integration technique. IEEE Trans. Magn. 40(2), 1334–1337 (2004). https://doi.org/10.1109/TMAG.2004.824536

    Article  Google Scholar 

  37. De Gersem, H., Hameyer, K., Weiland, T.: Field-circuit coupled models in electromagnetic simulation. J. Comput. Appl. Math. 168(1-2), 125–133 (2004). https://doi.org/10.1016/j.cam.2003.05.008

    Article  MathSciNet  MATH  Google Scholar 

  38. Deschamps, G.A.: Electromagnetics and differential forms. Proc. IEEE 69(6), 676–696 (1981). https://doi.org/dx.doi.org/10.1109/PROC.1981.12048

    Article  Google Scholar 

  39. Dirks, H.K.: Quasi-stationary fields for microelectronic applications. Electr. Eng. 79(2), 145–155 (1996). https://doi.org/10.1007/BF01232924

    Article  Google Scholar 

  40. Dutiné, J.S., Richter, C., Jörgens, C., Schöps, S., Clemens, M.: Explicit time integration techniques for electro- and magneto-quasistatic field simulations. In: Graglia, R.D. (ed.) Proceedings of the International Conference on Electromagnetics in Advanced Applications (ICEAA) 2017. IEEE, New York (2017). https://doi.org/10.1109/ICEAA.2017.8065562

    Google Scholar 

  41. Dyck, D.N., Webb, J.P.: Solenoidal current flows for filamentary conductors. IEEE Trans. Magn. 40(2), 810–813 (2004). https://doi.org/10.1109/TMAG.2004.824594

    Article  Google Scholar 

  42. Eller, M., Reitzinger, S., Schöps, S., Zaglmayr, S.: A symmetric low-frequency stable broadband Maxwell formulation for industrial applications. SIAM J. Sci. Comput. 39(4), B703–B731 (2017). https://doi.org/10.1137/16M1077817

    Article  MathSciNet  MATH  Google Scholar 

  43. Estévez Schwarz, D.: Consistent initialization of differential-algebraic equations in circuit simulation. Technical Report 99-5, Humboldt Universität Berlin, Berlin (1999)

    Google Scholar 

  44. Gödel, N., Schomann, S., Warburton, T., Clemens, M.: GPU accelerated Adams-Bashforth multirate discontinuous Galerkin FEM simulation of high-frequency electromagnetic fields. IEEE Trans. Magn. 46(8), 2735–2738 (2010)

    Article  Google Scholar 

  45. Griffiths, D.F.: Introduction to Electrodynamics. Prentice-Hall, Upper Saddle River (1999)

    Google Scholar 

  46. Hahne, P., Weiland, T.: 3d eddy current computation in the frequency domain regarding the displacement current. IEEE Trans. Magn. 28(2), 1801–1804 (1992). https://doi.org/10.1109/20.124056

    Article  Google Scholar 

  47. Hairer, E., Nørsett, S.P., Wanner, G.: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer Series in Computational Mathematics, 2 edn. Springer, Berlin (2002)

    Google Scholar 

  48. Harrington, R.F.: Field Computation by Moment Methods. Wiley-IEEE, New York (1993)

    Book  Google Scholar 

  49. Haus, H.A., Melcher, J.R.: Electromagnetic Fields and Energy. Englewood Cliffs, Prentice-Hall (1989)

    Google Scholar 

  50. Heaviside, O.: On the forces, stresses, and fluxes of energy in the electromagnetic field. Proc. R. Soc. Lond. Ser. I 50, 126–129 (1891)

    MATH  Google Scholar 

  51. Hehl, F.W., Obukhov, Y.N.: Foundations of Classical Electrodynamics – Charge, Flux, and Metric. Progress in Mathematical Physics. Birkhäuser, Basel (2003)

    Chapter  MATH  Google Scholar 

  52. Heise, B.: Analysis of a fully discrete finite element method for a nonlinear magnetic field problem. SIAM J. Numer. Anal. 31(3), 745–759 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  53. Hesthaven, J.S., Warburton, T.: Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Texts in Applied Mathematics. Springer, New York (2008)

    Book  MATH  Google Scholar 

  54. Jackson, J.D.: Classical Electrodynamics, 3rd edn. Wiley, New York (1998)

    MATH  Google Scholar 

  55. Jochum, M.T., Farle, O., Dyczij-Edlinger, R.: A new low-frequency stable potential formulation for the finite-element simulation of electromagnetic fields. IEEE Trans. Magn. 51(3), 7402,304 (2015). https://doi.org/10.1109/TMAG.2014.2360080

    Article  MATH  Google Scholar 

  56. Kameari, A.: Calculation of transient 3D eddy-current using edge elements. IEEE Trans. Magn. 26(5), 466–469 (1990). https://doi.org/10.1109/20.106354

    Article  Google Scholar 

  57. Kerler-Back, J., Stykel, T.: Model reduction for linear and nonlinear magneto-quasistatic equations. Int. J. Numer. Methods Eng. 111(13), 1274–1299 (2017). https://doi.org/10.1002/nme.5507

    Article  MathSciNet  Google Scholar 

  58. Koch, S., Weiland, T.: Time domain methods for slowly varying fields. In: URSI International Symposium on Electromagnetic Theory (EMTS 2010), pp. 291–294 (2010). https://doi.org/10.1109/URSI-EMTS.2010.5636991

  59. Koch, S., Weiland, T.: Different types of quasistationary formulations for time domain simulations. Radio Sci. 46(5) (2011). https://doi.org/10.1029/2010RS004637

    Article  Google Scholar 

  60. Lamour, R., März, R., Tischendorf, C.: Differential-Algebraic Equations: A Projector Based Analysis. Differential-Algebraic Equations Forum. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-27555-5

    Book  MATH  Google Scholar 

  61. Larsson, J.: Electromagnetics from a quasistatic perspective. Am. J. Phys. 75(3), 230–239 (2007). https://doi.org/10.1119/1.2397095

    Article  Google Scholar 

  62. Manges, J.B., Cendes, Z.J.: Tree-cotree decompositions for first-order complete tangential vector finite elements. Int. J. Numer. Methods Eng. 40(9), 1667–1685 (1997). https://doi.org/10.1002/(SICI)1097-0207(19970515)40:9<1667::AID-NME133>3.0.CO;2-9

    Article  MathSciNet  Google Scholar 

  63. März, R.: Differential algebraic systems with properly stated leading term and MNA equations. In: Anstreich, K., Bulirsch, R., Gilg, A., Rentrop, P. (eds.) Modelling, Simulation and Optimization of Integrated Circuits, pp. 135–151. Birkhäuser, Berlin (2003)

    Chapter  MATH  Google Scholar 

  64. Maxwell, J.C.: A dynamical theory of the electromagnetic field. Phil. Trans. R. Soc. London CLV, 459–512 (1864)

    Google Scholar 

  65. Mehrmann, V.: Index Concepts for Differential-Algebraic Equations, pp. 676–681. Springer, Berlin (2015). https://doi.org/10.1007/978-3-540-70529-1_120

    Chapter  Google Scholar 

  66. Merkel, M., Niyonzima, I., Schöps, S.: Paraexp using leapfrog as integrator for high-frequency electromagnetic simulations. Radio Sci. 52(12), 1558–1569 (2017). https://doi.org/10.1002/2017RS006357

    Article  Google Scholar 

  67. Monk, P.: Finite Element Methods for Maxwell’s Equations. Oxford University Press, Oxford (2003)

    Book  MATH  Google Scholar 

  68. Monk, P., Süli, E.: A convergence analysis of Yee’s scheme on nonuniform grids. SIAM J. Numer. Anal. 31(2), 393–412 (1994). https://doi.org/10.1137/0731021

    Article  MathSciNet  MATH  Google Scholar 

  69. Munteanu, I.: Tree-cotree condensation properties. ICS Newsl. (International Compumag Society) 9, 10–14 (2002). http://www.compumag.org/jsite/images/stories/newsletter/ICS-02-09-1-Munteanu.pdf

  70. Nagel, L.W., Pederson, D.O.: Simulation program with integrated circuit emphasis. Technical Report, University of California, Berkeley, Electronics Research Laboratory, ERL-M382 (1973)

    Google Scholar 

  71. Nédélec, J.C.: Mixed finite elements in r 3. Numer. Math. 35(3), 315–341 (1980). https://doi.org/10.1007/BF01396415

    Article  MathSciNet  MATH  Google Scholar 

  72. Nicolet, A., Delincé, F.: Implicit Runge-Kutta methods for transient magnetic field computation. IEEE Trans. Magn. 32(3), 1405–1408 (1996). https://doi.org/0.1109/20.497510

    Article  Google Scholar 

  73. Ostrowski, J., Hiptmair, R., Krämer, F., Smajic, J., Steinmetz, T.: Transient full Maxwell computation of slow processes. In: Michielsen, B., Poirier, J.R. (eds.) Scientific Computing in Electrical Engineering SCEE 2010. Mathematics in Industry, vol. 16, pp. 87–95. Springer, Berlin (2012). https://doi.org/10.1007/978-3-642-22453-9_10

    Chapter  Google Scholar 

  74. Ouédraogo, Y., Gjonaj, E., Weiland, T., De Gersem, H., Steinhausen, C., Lamanna, G., Weigand, B., Preusche, A., Dreizler, A., Schremb, M.: Electrohydrodynamic simulation of electrically controlled droplet generation. Int. J. Heat Fluid Flow 64, 120–128 (2017)

    Article  Google Scholar 

  75. Petzold, L.R.: Differential/algebraic equations are not ODE’s. SIAM J. Sci. Stat. Comput. 3(3), 367–384 (1982). https://doi.org/10.1137/0903023

    Article  MathSciNet  MATH  Google Scholar 

  76. Rapetti, F., Rousseaux, G.: On quasi-static models hidden in Maxwell’s equations. Appl. Numer. Math. 79, 92–106 (2014). https://doi.org/10.1016/j.apnum.2012.11.007

    Article  MathSciNet  MATH  Google Scholar 

  77. Rautio, J.C.: The long road to Maxwell’s equations. IEEE Spectr. 51(12), 36–56 (2014). https://doi.org/10.1109/MSPEC.2014.6964925

    Article  Google Scholar 

  78. Raviart, P.A., Thomas, J.M.: Primal hybrid finite element methods for 2nd order elliptic equations. Math. Comput. 31(138), 391–413 (1977)

    MATH  Google Scholar 

  79. Ruehli, A.E.: Equivalent circuit models for three-dimensional multiconductor systems. IEEE Trans. Microwave Theory Tech. 22(3), 216–221 (1974)

    Article  Google Scholar 

  80. Ruehli, A.E., Antonini, G., Jiang, L.: The Partial Element Equivalent Circuit Method for Electro-Magnetic and Circuit Problems. Wiley, Hoboken (2015)

    Google Scholar 

  81. Schilders, W.H.A., Ciarlet, P., ter Maten, E.J.W. (eds.): Handbook of Numerical Analysis. Numerical Methods in Electromagnetics. Handbook of Numerical Analysis, vol. 13. North-Holland, Amsterdam (2005)

    Google Scholar 

  82. Schmidt, K., Sterz, O., Hiptmair, R.: Estimating the eddy-current modeling error. IEEE Trans. Magn. 44(6), 686–689 (2008). https://doi.org/10.1109/TMAG.2008.915834

    Article  Google Scholar 

  83. Schoenmaker, W.: Computational Electrodynamics. River Publishers Series in Electronic Materials and Devices. River Publishers, Delft (2017)

    Google Scholar 

  84. Schöps, S.: Multiscale modeling and multirate time-integration of field/circuit coupled problems. Dissertation, Bergische Universität Wuppertal & Katholieke Universiteit Leuven, Düsseldorf (2011). VDI Verlag. Fortschritt-Berichte VDI, Reihe 21

    Google Scholar 

  85. Schöps, S., Bartel, A., Clemens, M.: Higher order half-explicit time integration of eddy current problems using domain substructuring. IEEE Trans. Magn. 48(2), 623–626 (2012). https://doi.org/10.1109/TMAG.2011.2172780

    Article  Google Scholar 

  86. Schöps, S., De Gersem, H., Weiland, T.: Winding functions in transient magnetoquasistatic field-circuit coupled simulations. Int. J. Comput. Math. Electr. Electron. Eng. 32(6), 2063–2083 (2013). https://doi.org/10.1108/COMPEL-01-2013-0004

    Article  MathSciNet  MATH  Google Scholar 

  87. Schuhmann, R., Weiland, T.: Conservation of discrete energy and related laws in the finite integration technique. Prog. Electromagn. Res. 32, 301–316 (2001). https://doi.org/10.2528/PIER00080112

    Article  Google Scholar 

  88. Schuhmacher, S., Klaedtke, A., Keller, C., Ackermann, W., De Gersem, H.: Optimizing the inductance cancellation behavior in an EMI filter design with the help of a sensitivity analysis. In: EMC Europe. Angers, France (2017)

    Google Scholar 

  89. Steinmetz, T., Kurz, S., Clemens, M.: Domains of validity of quasistatic and quasistationary field approximations. Int. J. Comput. Math. Electr. Electron. Eng. 30(4), 1237–1247 (2011). https://doi.org/10.1108/03321641111133154

    Article  MathSciNet  MATH  Google Scholar 

  90. Taflove, A.: Computational Electrodynamics: The Finite-Difference Time-Domain-Method. Artech House, Dedham (1995)

    Google Scholar 

  91. Taflove, A.: A perspective on the 40-year history of FDTD computational electrodynamics. Appl. Comput. Electromagn. Soc. J. 22(1), 1–21 (2007)

    Google Scholar 

  92. Tischendorf, C.: Topological index calculation of DAEs in circuit simulation. Technical Report 3-4, Humboldt Universität Berlin, Berlin (1999)

    Google Scholar 

  93. Tonti, E.: On the formal structure of physical theories. Technical Report, Politecnico di Milano, Milano, Italy (1975)

    Google Scholar 

  94. Tsukerman, I.A.: Finite element differential-algebraic systems for eddy current problems. Numer. Algorithms 31(1), 319–335 (2002). https://doi.org/10.1023/A:1021112107163

    Article  MathSciNet  MATH  Google Scholar 

  95. Webb, J.P., Forghani, B.: The low-frequency performance of h − ϕ and t − ω methods using edge elements for 3d eddy current problems. IEEE Trans. Magn. 29(6), 2461–2463 (1993). https://doi.org/10.1109/20.280983

    Article  Google Scholar 

  96. Weeks, W., Jimenez, A., Mahoney, G., Mehta, D., Qassemzadeh, H., Scott, T.: Algorithms for ASTAP – a network-analysis program. IEEE Trans. Circuit Theory 20(6), 628–634 (1973). https://doi.org/10.1109/TCT.1973.1083755

    Article  Google Scholar 

  97. Weiland, T.: A discretization method for the solution of Maxwell’s equations for six-component fields. Int. J. Electron. Commun. (AEU) 31, 116–120 (1977)

    Google Scholar 

  98. Weiland, T.: On the unique numerical solution of Maxwellian eigenvalue problems in three dimensions. Part. Accel. 17(227–242) (1985)

    Google Scholar 

  99. Weiland, T.: Time domain electromagnetic field computation with finite difference methods. Int. J. Numer. Modell. Electron. Networks Devices Fields 9(4), 295–319 (1996). https://doi.org/10.1002/(SICI)1099-1204(199607)9:4<295::AID-JNM240>3.0.CO;2-8

    Article  Google Scholar 

  100. Yee, K.S.: Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Trans. Antennas Propag. 14(3), 302–307 (1966). https://doi.org/10.1109/TAP.1966.1138693

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität Darmstadt, Graduate School of Computational Engineering, Darmstadt, Germany

    Idoia Cortes Garcia, Sebastian Schöps & Herbert De Gersem

  2. Universität zu Köln, Mathematisches Institut, Köln, Germany

    Sascha Baumanns

Authors
  1. Idoia Cortes Garcia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sebastian Schöps
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Herbert De Gersem
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sascha Baumanns
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sebastian Schöps .

Editor information

Editors and Affiliations

  1. Department of Mathematics, North Carolina State University, Raleigh, NC, USA

    Stephen Campbell

  2. Institut für Mathematik, Technische Universität Ilmenau, Ilmenau, Germany

    Achim Ilchmann

  3. Institut für Mathematik, Technische Universität Berlin, Berlin, Germany

    Volker Mehrmann

  4. Fachbereich Mathematik, Universität Hamburg, Hamburg, Germany

    Timo Reis

Rights and permissions

Reprints and permissions

Copyright information

© 2018 © Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Cortes Garcia, I., Schöps, S., De Gersem, H., Baumanns, S. (2018). Systems of Differential Algebraic Equations in Computational Electromagnetics. In: Campbell, S., Ilchmann, A., Mehrmann, V., Reis, T. (eds) Applications of Differential-Algebraic Equations: Examples and Benchmarks. Differential-Algebraic Equations Forum. Springer, Cham. https://doi.org/10.1007/11221_2018_8

Download citation

Publish with us

Policies and ethics

Search

Navigation