Model Exchange

[AC/DC V3.5a] Maxwell Stress Tensor "pitfall" example

Ivar KJELBERG, CSEM sa

The Maxwell Stress Tensor is handy to use to calculate forces on magnets, but the method is very very sensitive to meshing symmetry. This example show the effect of surrounding a square magnet by a circle (GEOM1) and mesh rather fine with triangular free mesh.

The maxwell Stress Tensor calulation is rather wrong.

In GEOM2 the same model is meshed with a rough square mesh and the result is coherent to > 10 digits !

Why ?
The stress tensor aproach derives the force by integrating the divergence of the field along the edges of the Magnet (in this case), the resulting force can be rather large per edge side (try selecting separately left and right vertical edge for your Boundary Edge integrations), but often the force cancel out by an opposite value on the other symmetric edge.
However, it is well known that the numerical error winds up when one do differences of two large numbers almost identical in value.

Conclusions for me: use only square meshes and rely on symmetry when dealing with the Maxwell Stress Tensor.

And as usual: carefully check your models, verify and validate them

For more on the theory on Maxwell Stress Tensor: take a look at the COMSOL documentation or i.e.: "Introduction to Electrodynamics", 3rd Ed, D.J. Griffiths, PrenticeHall 1981, ISBN 0-13-805326-X

Other Entries by This Contributor

• [SM 3.5a] 3D Euler Beam Properties Calculations
• Zernike Polynomial extraction of deformed optical surface
• [SM v3.5a] Rotation constraints in structural module. With complements

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