Abstract
A brief outline of some common characteristics of the computation of constitutive equations is presented hereafter and the formulation of the constitutive problem will then be detailed for two different kinds of discretization: structured and unstructured. The thermal problem is used as an example of one kind of formulation, whereas the magneto-static problem is employed to introduce another material link formulation.
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References
Bossavit, A., Kettunen, L.: Yee-like schemes on staggered cellular grids: A synthesis between FIT and FEM approaches. IEEE Transaction on Magnetics 36(4), 861–867 (2000)
Bossavit, A.: Generating whitney forms of polynomial degree one and higher. IEEE Transaction on Magnetics 38(2), 341–344 (2002)
Codecasa, L., Specogna, R., Trevisan, F.: Symmetric positive-definite constitutive matrices for discrete eddy-current problems. IEEE Transactions on Magnetics 43(2), 510–515 (2007)
Marrone, M.: A new consistent way to build symmetric constitutive matrices on general 2-d grids. IEEE Transactions on Magnetics 40(2), 1420–1423 (2004)
Binns, K.J., Lawrenson, P.J., Trowbridge, C.W.: The analytical and numerical solution of electric and magnetic fields. Wiley (1995)
Giuffrida, C., Gruosso, G., Repetto, M.: Finite formulation of nonlinear magneto-statics with integral boundary conditions. IEEE Transactions on Magnetics 42(5), 1503–1511 (2006)
Repetto, M., Trevisan, F.: Global formulation for 3D magneto-static using flux and gauged potential approaches. Int. Journal on Numerical Methods in Engineering 60, 755–772 (2004)
Whitney, H.: Geometric Integration Theory. Princeton University Press, Princeton (1957)
Bossavit, A.: Computational electromagnetism. Academic Press (1998)
Schuhmann, R., Schmidt, P., Weiland, T.: A new whitney-based material operator for the finite-integration technique on triangular grids. IEEE Transaction on Magnetics 38(2), 409–412 (2002)
Castillo, P., Koning, J., Rieben, R., Stowell, M., White, D.: Discrete differential forms: A novel methodology for robust computational electromagnetics. Technical Report UCRL-ID-151522, Lawrence Livermore National Laboratory (2003)
Alotto, P., Perugia, I.: Matrix properties of a vector potential cell method for magnetostatics. IEEE Transactions on Magnetics 40(2), 1045–1048 (2004)
Alotto, P., Specogna, R., Trevisan, F.: A θ-method for eddy currents in time-domain with a discrete geometric approach. IEEE Transaction on Magnetics 42(4), 779–782 (2006)
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Alotto, P., Freschi, F., Repetto, M., Rosso, C. (2013). Constitutive Equations. In: The Cell Method for Electrical Engineering and Multiphysics Problems. Lecture Notes in Electrical Engineering, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36101-2_3
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DOI: https://doi.org/10.1007/978-3-642-36101-2_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36100-5
Online ISBN: 978-3-642-36101-2
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