Silicom has successfully used Elmer software to characterize 3D transversal magnetic field in Czochralski silicon crystal growth.

In a customer project, electromagnetics equations (a form of Maxwell equations) were solved, and a full-scale geometrical configuration consisted of two separate magnets (dimensions 1.5m) and a covering iron layer.

In the model, iron permeability was formulated with nonlinear BH-curve. The model consisted of 450 000 tetrahedra, and was run on Ubuntu (Inter Pentium, 2.3GHz) in serial mode in 35 minutes.

Figure: 3D solution for magnetic flux density

Elmer furher information, see http://www.csc.fi/elmer.