Extrusion, contraction: their discretization via Whitney forms

Extrusion, contraction: their discretization via Whitney forms The v×B term in eddy current equations for conducting fluids is an instance of contraction of a differential form by a vector field. We search for a natural way to discretize such contractions. Looking at the operation of extrusion of a manifold, which is dual to contraction, provides the main clue. Two example applications, Carpenter's gauge and Eulerian computations in MHD problems, are suggested. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

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Publisher
Emerald Publishing
Copyright
Copyright © 2003 MCB UP Ltd. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640310474877
Publisher site
See Article on Publisher Site

Abstract

The v×B term in eddy current equations for conducting fluids is an instance of contraction of a differential form by a vector field. We search for a natural way to discretize such contractions. Looking at the operation of extrusion of a manifold, which is dual to contraction, provides the main clue. Two example applications, Carpenter's gauge and Eulerian computations in MHD problems, are suggested.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Sep 1, 2003

Keywords: Contraction; Extrusion; Generalized finite differences; Whitney forms; Gauging; Magnetohydrodynamics

References

  • Magnetostatic field computations in terms of two‐component vector potentials
    Albanese, L.; Rubinacci, G.
  • Time domain electromagnetic field computation with finite difference methods

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