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


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

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User Comments

Shu Zhou
Oct 8, 2009 at 9:20am UTC

Very useful, Thanks!

Scott Clark
Mar 14, 2010 at 11:14pm UTC

Good comment! Thanks

aboozar ghafari
Apr 6, 2010 at 5:28pm UTC

Comment removed by aboozar ghafari.

aboozar ghafari
Apr 6, 2010 at 5:59pm UTC

I tried to open it in COMSOL 3.5 but I encountered this message:File created by a later version of COMSOL. is there any solution for this problem?
Thank you.

Diana Strickland
May 7, 2010 at 7:45pm UTC

Thank you for the comment, Ivar.

I'll clarify something, in case someone new to modeling is reading. By 'coherent', I think Ivar means that, with only a magnet present (nothing to pull on) there should be no force. Yet his Geom1 with triangle mesh yields ~0.2N force. The square mesh (Geom2) yields ~e-14 or better--very close to the expected zero force.

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