Existence results for the A – φ – B magnetodynamic formulation of the Maxwell system with skin and proximity effects

References

• Alonso Rodríguez A, Valli A. Eddy current approximation of Maxwell equations. MS & A. Modeling, simulation and applications. Milan: Springer-Verlag Italia; 2010. (Theory, algorithms and applications; 4).
   Google Scholar
• Bossavit A. Computational electromagnetism. Electromagnetism. San Diego (CA): Academic Press, Inc.; 1998. (Variational formulations, complementarity, edge elements).
   Google Scholar
• Alonso Rodríguez A, Hiptmair R, Valli A. A hybrid formulation of eddy current problems. Numer Methods Partial Differ Equ. 2005;21(4):742–763.
   Web of Science ®Google Scholar
• Meunier G. The finite element method for electromagnetic modeling. London: ISTE; 2008. Translated from the 2008 French original.
   Google Scholar
• Amrouche C, Bernardi C, Dauge M, et al. Vector potentials in three-dimensional nonsmooth domains. Math Methods Appl Sci. 1998;21:823–864.
   Web of Science ®Google Scholar
• Nicaise S. Existence results for the A−φ magnetodynamic formulation of the Maxwell system. Appl Anal. 2015;94(5):863–878.
   Web of Science ®Google Scholar
• Creusé E, Nicaise S, Tittarelli R. Space-time residual-based a posteriori estimators for the A−φ magnetodynamic formulation of the Maxwell system. Comput Methods Appl Math. 2014;14(4):429–460.
   Web of Science ®Google Scholar
• Gyselinck J, Sabariego RV, Dular P. Time-domain homogenization of windings in 2-d finite elements models. IEEE Trans Mag. 2007;43(4):1297–1300.
   Web of Science ®Google Scholar
• Niyomsatian K, Gyselinck J, Sabariego RV. Time-domain homogenization of multiturn windings based on rl cauer ladder networks. Int J Numer Model: Electron Netw, Devices and Fields. EMF18 special issue; 2019.
   Google Scholar
• Sabariego RV, Dular P, Gyselinck J. Time-domain homogenization of windings in 3-D finite element models. IEEE Trans Mag. 2008;44(6):1302–1305.
   Web of Science ®Google Scholar
• Gyselinck J, Dular P. Frequency-domain homogenization of bundles of wires in 2-d magnetodynamic fe calculations. IEEE Trans Mag. 2005;41(5):1416–1419.
   Web of Science ®Google Scholar
• Nan X, Sullivan CR. An equivalent complex permeability model for litz-wire windings. IEEE Trans Ind Appl. 2008;45(2):854–860.
   Web of Science ®Google Scholar
• Igarashi H. Semi-analytical approach for finite-element analysis of multi-turn coil considering skin and proximity effects. IEEE Trans Mag. 2017;53(1):1–7.
   Web of Science ®Google Scholar
• Niyomsatian K, Gyselinck J, Sabariego R. Experimental extraction of winding resistance in litz-wire transformers – influence of winding mutual resistance. IEEE Trans Pow El. 2019;34(7):6736–6746.
   Web of Science ®Google Scholar
• Podoltsev A, Kucheryavaya I, Lebedev B. Analysis of effective resistance and eddy-current losses in multiturn winding of high-frequency magnetic components. IEEE Trans Mag. 2003;39(1):539–548.
   Web of Science ®Google Scholar
• Rossmanith H, Doebroenti M, Albach M, et al. Measurement and characterization of high frequency losses in nonideal litz wires. IEEE Trans Pow El. 2003;26(11):3386–3394.
   Google Scholar
• Weber C. A local compactness theorem for Maxwell's equations. Math Methods Appl Sci. 1980;2:12–25.
   Google Scholar
• Barbu V. Nonlinear differential equations of monotone types in Banach spaces. New York: Springer; 2010. (Springer Monographs in Mathematics).
   Google Scholar
• Brézis H. Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Amsterdam: North-Holland Publishing Co.; 1973. (North-Holland Mathematics Studies; 5. Notas de Matemática; 50).
   Google Scholar
• Showalter RE. Hilbert space methods for partial differential equations. London: Pitman; 1977. (Monographs and Studies in Mathematics; 1).
   Google Scholar
• Grisvard P. Elliptic problems in nonsmooth domains. Boston: Pitman; 1985. (Monographs and Studies in Mathematics; 24).
   Google Scholar
• Brezis H. Functional analysis, Sobolev spaces and partial differential equations. New York: Springer; 2011. (Universitext).
   Google Scholar
• Nicaise S, Tröltzsch F. A coupled Maxwell integrodifferential model for magnetization processes. Math Nachr. 2014;287(4):432–452.
   Web of Science ®Google Scholar