Abstract
Tonti diagrams highlight a common structure of several physical laws describing different phenomena. From a computational viewpoint, this underlying common structure allows to build topological operators (discrete counterpart of differential operators) only once, and they can be used to easily assemble the stiffness matrices and the coupling terms of the various problems. An application of this concept to the coupled electromagnetic-thermal problem of induction heating is presented in this work, taking into account the nonlinear effects of temperature on the magnetic characteristic beyond the Curie point.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Tonti, E.: Finite formulation of electromagnetic field. IEEE Trans. Magn. 38, 333–336 (2002)
Tonti, E.: Discrete physics. http://www.dic.units.it/perspage/discretephysics/
Eymard, R., Gallouët, T., Herbin, R.: Finite volume methods. In: Ciarlet, P., Lions, J. (eds.) Handbook of Numerical Analysis, vol. VII, pp. 713–1020. North-Holland/Elsevier, Amsterdam (2000)
Yee, K.: Numerical solution of boundary value problems involving Maxwell equations in isotropic media. IEEE Trans. Antenn. Propag. AP-14, 302–307 (1966)
Weiland, T.: A discretization method for the solution of Maxwell’s equations for six-components fields. Electron. Comm. AEUE 31, 116–120 (1977)
Repetto, M., Trevisan, F.: Global formulation for 3D magneto-static using flux and gauged potential approaches. Int. J. Numer. Meth. Eng. 60, 755–772 (2004)
Specogna, R., Trevisan, F.: Discrete constitutive equations in a − χ geometric eddy-current formulation. IEEE Trans. Magn. 41(4), 1259–1263 (2005)
Codecasa, L., Specogna, R., Trevisan, F.: Symmetric positive-definite constitutive matrices for discrete eddy-current problems. IEEE Trans. Magn. 43(2), 510–515 (2007)
Aliferov, A., Dughiero, F., Forzan, M.: Coupled magneto-thermal FEM model of direct heating of ferromagnetic bended tubes. IEEE Trans. Magn. 46(8), 3217–3220 (2010)
Canova, A., Dughiero, F., Fasolo, F., Forzan, M., Freschi, F., Giaccone, L., Repetto, M.: Simplified approach for 3d nonlinear induction heating problems. IEEE Trans. Magn. 45(3), 1855–1858 (2009)
Du Terrail, Y., Sabonnadiere, J., Masse, P., Coulomb, J.: Nonlinear complex finite elements analysis of electromagnetic field in steady-state AC devices. IEEE Trans. Magn. 20(4), 549–552 (1984)
Alotto, P., Freschi, F., Repetto, M.: Multiphysics problems via the cell method: The role of tonti diagrams. IEEE Trans. Magn. 46(8), 2959–2962 (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Freschi, F., Repetto, M. (2012). Tonti Diagrams and Algebraic Methods for the Solution of Coupled Problems. In: Michielsen, B., Poirier, JR. (eds) Scientific Computing in Electrical Engineering SCEE 2010. Mathematics in Industry(), vol 16. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22453-9_21
Download citation
DOI: https://doi.org/10.1007/978-3-642-22453-9_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-22452-2
Online ISBN: 978-3-642-22453-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)