How to Define the Minimum Set of Equations for Edge Elements *

Abstract

The use of edge or facet elements for electromagnetic field computation leads to an immediate question: What is the minimum set of equations and how can it be defined? For instance, in the case of static magnetic fields Maxwell's equations constrain the line integrals of the magnetic field and the surface integrals of the magnetic flux density over closed loops and surfaces. This means that not all edges or facets of a mesh are independent since some of the coefficients related to them can be defined from the others. This leads to a practical question regarding definition of the set of independent equations and how to express the dependent equations in terms of the independent ones. This paper shows how to define a local basis and gives an algorithm to find a global minimum set of equations for edge elements. In addition the algorithm is enlarged to express dependent equations in terms of independent ones.

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