Eur. Phys. J. Appl. Phys.
Volume 39, Number 2, August 2007NUMELEC 2006
|Page(s)||133 - 141|
|Section||Magnetism and Superconductivity|
|Published online||28 June 2007|
The pairing matrix in discrete electromagnetism
CERN AT/MEL, 1211 Geneva 23, Switzerland
2 ETAS GmbH, Stuttgart, Germany
Corresponding author: firstname.lastname@example.org
Revised: 19 March 2007
Accepted: 3 April 2007
Published online: 28 June 2007
We introduce pairing matrices on simplicial cell complexes in discrete electromagnetism as a means to avoid the explicit construction of a topologically dual complex. Interestingly, the Finite Element Method with first-order Whitney elements — when it is looked upon from a cell-method perspective — features pairing matrices and thus an implicitly defined dual mesh. We show that the pairing matrix can be used to construct discrete energy products. In this exercise we find that different formalisms lead to equivalent matrix representations. Discrete de Rham currents are an elegant way to subsume these geometrically equivalent but formally distinct ways of defining energy-products.
PACS: 02.40.Sf – Manifolds and cell complexes / 02.70.Dh – Finite-element and Galerkin methods / 41.20.Gz – Magnetostatics; magnetic shielding, magnetic induction, boundary-value problems
© EDP Sciences, 2007
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