Cross Product

In the instance where there are two fields (F,G) defined on the same unit cell we can take the cross product of the fields. The cross product of these edge-defined fields is shown in the following example. First, the cross product of the fields along the red edges is taken to give the resulting blue vector.

The formula for this operation on the red field is

$\begin{equation} (F \times G)_{x} = (F_{y} G_{z} - F_{ z} G_{ y}) \end{equation}$

Next, on the oppposite side the cross product of violet fields (equation 1) to give the olive vector.

The olive and blue vectors are averaged to give the green vector.

The handling of shared edges is handled the same way as in the curl module.

Ryan McClarren

Last modified: Thu Aug 15 10:58:24 EDT 2002