Abstract
The idea of modelling space as two interacting equivalent networks, one for currents, one for magnetic fluxes, pervades computational electromagnetics since its beginnings. The Yee scheme, the TLM method, can thus be interpreted. But this is also true of finite element- or finite volume-inspired more recent proposals, as we show, so the idea is not incompatible with “unstructured” meshes. Yet, meshes with some rotational and translational symmetry (locally, at least) are desirable on many accounts. The tetrahedral Sommerville mesh we describe here, able to fit curved boundaries and yet regular, looks like an interesting compromise.
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
Bossavit, A.: ‘Generalized Finite Differences’ in computational electromagnetics, PIER 32 (F.L. Teixeira, ed.), EMW (Cambridge, Ma), 2001, pp. 45–64. http://ceta-mac1.mit.edu/pier/pier32/02.bossavit.pdf/pier/pier32/02.bossavit.pdf
Senechal, M.: Which Tetrahedra Fill Space? Math. Magazine, 4, 5 (1981), pp. 227–43.
Sommerville, D.M.Y.: Space-filling Tetrahedra in Euclidean Space. Proc. Edinburgh Math. Soc, 41 (1923), pp. 49–57.
Tonti, E.: A Direct Formulation of Field Laws: The Cell Method. CMES, 2, 2 (2001), pp. 237–58.
Weiland, T.: Time domain electromagnetic field computation with finite difference methods. Int. J. Numer. Modelling, 9(1996), pp. 295–319.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bossavit, A. (2004). The Sommerville Mesh in Yee-like Schemes. In: Schilders, W.H.A., ter Maten, E.J.W., Houben, S.H.M.J. (eds) Scientific Computing in Electrical Engineering. Mathematics in Industry, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55872-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-55872-6_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21372-7
Online ISBN: 978-3-642-55872-6
eBook Packages: Springer Book Archive