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# Re: discontinuities in stress tensor mask in thin air

- To: femm@yahoogroups.com
- Subject: Re: discontinuities in stress tensor mask in thin air
- From: "mikeshonle" <mike@psychonic.net>
- Date: Fri, 14 Mar 2003 02:34:11 -0000
- In-reply-to: <3E6D0CB4.6070600@ieee.org>
- User-agent: eGroups-EW/0.82

    Hi, Dave, thanks for your detailed analysis and response. I have
    been doing some more experimenting, and have come up with the
    following:
    First, I tried to replicate your results for the axisymmetric case,
    and I got exactly the same number using the line integral method but
    doing the WST method, I got .65 instead of .59.

    Also, I went back and used the line integral in my test cases, and
    got much more consistant (vs. changing mesh spacing) results (within
    about 2% instead of 30% !). I also re-ran my moving magnet
    experiment and it was completely monotonic and almost completely
    monotonic in the derivative as well.

    Let me know if you would like my project file in case you would have
    a chance to take a look and see if I'm doing anything wrong. As a
    test, I've been varying the mesh spacing in the region just outside
    the region that has the magnets, and that changes the computed force
    by a lot (as well as showing the "diffraction" of the force tensor
    lines).

    Also, B.T.W, would you happen to know what the density of NIB 37 is?

    Thanks so much for you help, and let me know if you need any more
    information.

    Thanks,
    -Mike

    --- In femm@yahoogroups.com, David Meeker <dmeeker@i...> wrote:
    > 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@i...
    > www: http://femm.berlios.de/dmeeker

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  - Re: [femm] discontinuities in stress tensor mask in thin air
    - From: David Meeker <dmeeker@ieee.org>

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