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# Re: [femm] discontinuities in stress tensor mask in thin air

- To: femm@yahoogroups.com
- Subject: Re: [femm] discontinuities in stress tensor mask in thin air
- From: David Meeker <dmeeker@ieee.org>
- Date: Mon, 10 Mar 2003 17:07:48 -0500
- In-reply-to: <b4iqeq+qh17@eGroups.com>
- References: <b4iqeq+qh17@eGroups.com>
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`This is sort of an interesting problem, because it is possible to write down a simple analytical solution for the force between two magnets if they are idealized as dipoles (a good approximation if the magnets are fairly far away from one another). This result can then be used to sanity-check the results from femm. The results from femm shouldn't be exactly the same as the analyitcal solution (because the magnets aren't really point dipoles), but the analytical result should be pretty close to the finite element one.`
`I've attached a zip file containing a two sample problems looking at the on-axis interaction between two magnets in free space. One is 2D planar, and the other is axisymmetric. There is also a Mathcad worksheet (saved as Version 7) that has the analytical solution for the force, as well as a the force results for various mesh densities. There is also a pdf printout of the Mathcad worksheet.`
`A couple of things to note: The interaction forces are really quite weak, which makes it harder to get good force results. The force between dipoles has a (1/distance)^4 dependency for axisymmetric problems, and a (1/distance^3) dependency for 2D planar problems. Second, in this case, there is an obviously "good" contour for a stress tensor surface integral--one that pretty much follows the line that bisects the two magnets.`
`Anyhow, in both cases, things converge to solutions that are within a couple percent of the of the dipole approximation with increasing mesh density. Somewhat amusingly, the stress tensor surface integral has a faster rate of convergence in this case. I think that what is going on is that I'm using the "best possible" contour for the stress tensor surface integral, whereas the volume integral gets somewhat polluted by less accurate field values near the surface of the permanent magnets (where the field changes its strength and direction relatively suddenly). I should probably head-scratch a little bit more about how the program computes the weighting function used for the volume stress tensor integration (i.e. use one that is explicitly derived from a posteriori error estimates or something so that the surfaces of the PMs are avoided, perhaps like in the McFee paper).`

    Dave.
    --
    David Meeker
    email: dmeeker@ieee.org
    www: http://femm.berlios.de/dmeeker

Attachment: `zip00048.zip`
Description: Zip archive

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