https://doi.org/10.1051/epjap:2007074
The pairing matrix in discrete electromagnetism
1
CERN AT/MEL, 1211 Geneva 23, Switzerland
2
ETAS GmbH, Stuttgart, Germany
Corresponding author: bernhard.auchmann@cern.ch
Received:
18
January
2007
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
