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# Re: [femm] eddy-curr in a tube

- To: femm@yahoogroups.com
- Subject: Re: [femm] eddy-curr in a tube
- From: David Meeker <dmeeker@foster-miller.com>
- Date: Tue, 10 Apr 2001 09:46:03 -0400
- Organization: Foster-Miller, Inc.
- References: <NDBBLBMGALJCJOAGCHEBAEOKCEAA.mcgee@mcmillan-mcgee.com>

    McGee wrote:

    > Excellent Presentation of the example. For the boundary conditions,
    > is there a theoretical justification to weight the interpolation
    > values differently to obtain a better answer using finite element. I
    > have developed a FDTD model for my PhD work and I come upon the exact
    > same result you did. Since I was modeled the B and H fields around a
    > particular hysteresis loop it was critically important to ensure that
    > the boundary conditions were properly modeled. In the interpolation
    > of the grid I weighted the interior values more heavily than the
    > exterior values and obtained good results (a 1/3 2/3 rule seemed to
    > work best). Unfortunately I did not have the scope to explore the
    > numerical physics behind the choice of these weighting coefficients.
    > Anyway, I find that your model does a really great job. Any plans to
    > incorporate hysteresis effects. Bruce

    Well, what's going on with H is a product of using 3-node triangular
    elements. With these elements, the flux density is approximated as
    constant over the element, so it intrinsically doesn't represent areas
    where there are high gradients in B or H very well. Femm just uses a
    smoothing algorithm to make things look continuous. It works well away
    from boundaries, but at the boundaries, the smoothed result is really no
    better than the original constant-over-the element approximation.
    Higher-order elements (or in your case, a stencil with more points)
    might fix this, as would a denser mesh. There are several papers out
    there on "superconvergence" that try to get good results at boundaries,
    too, but I haven't run across an scheme that was really robust when
    actually implemented. Those scheme tend to extrapolate from values in
    interior elements, and it's easy to run into situations where the
    extrapolation goes berzerk or is ill-conditioned.

    Anyhow, I don't plan on implementing an really elaborate hysteresis
    model right away. Currently, a simple model of hysteresis is included
    in harmonic problems--the \phi_h in the material property dialog is the
    "hysteresis angle," which is a phase lag between B and H that is
    frequency-independent. This is sort of a crude model, but I've found it
    to be an useful way of approximating the effects of hysteresis in some
    real-world problems that I have worked on.

    Dave.

    --------------3F00629D76F97211EDFA2FFB
    Content-Type: text/html; charset=us-ascii
    Content-Transfer-Encoding: 7bit

    <!doctype html public "-//w3c//dtd html 4.0 transitional//en">
    <html>
    &nbsp;
    <p>McGee wrote:
    <blockquote TYPE=CITE>&nbsp;<font color="#0000FF"><font size=-1>Excellent
    Presentation of the example.&nbsp; For the boundary conditions, is there
    a theoretical justification to weight the interpolation values differently
    to obtain a better answer using finite element.&nbsp; I have developed
    a FDTD model for my PhD work and I come upon the exact same result you
    did.&nbsp; Since I was modeled the B and H fields around a particular hysteresis
    loop it was critically important to ensure that the boundary conditions
    were properly modeled.&nbsp; In the interpolation of the grid I weighted
    the interior values more heavily than the exterior values and obtained
    good results (a 1/3 2/3 rule seemed to work best).&nbsp; Unfortunately
    I did not have the scope to explore the numerical physics behind the choice
    of these weighting coefficients.&nbsp; Anyway, I find that your model does
    a really great job.&nbsp; Any plans to incorporate hysteresis effects.</font></font>&nbsp;<font color="#0000FF"><font size=-1>Bruce</font></font><tt></tt></blockquote>
    Well, what's going on with H is a product of using 3-node triangular elements.&nbsp;
    With these elements, the flux density is approximated as constant over
    the element, so it intrinsically doesn't represent areas where there are
    high gradients in B or H very well.&nbsp; Femm just uses a smoothing algorithm
    to make things look continuous.&nbsp; It works well away from boundaries,
    but at the boundaries, the smoothed result is really no better than the
    original constant-over-the element approximation.&nbsp; Higher-order elements
    (or in your case, a stencil with more points) might fix this, as would
    a denser mesh.&nbsp; There are several papers out there on "superconvergence"
    that try to get good results at boundaries, too, but I haven't run across
    an scheme that was really robust when actually implemented. Those scheme
    tend to extrapolate from values in interior elements, and it's easy to
    run into situations where the extrapolation goes berzerk or is ill-conditioned.
    <p>Anyhow, I don't plan on implementing an really elaborate hysteresis
    model right away.&nbsp; Currently, a simple model of hysteresis is included
    in harmonic problems--the \phi_h in the material property dialog is the
    "hysteresis angle," which is a phase lag between B and H that is frequency-independent.&nbsp;
    This is sort of a crude model, but I've found it to be an useful way of
    approximating the effects of hysteresis in some real-world problems that
    I have worked on.
    <p>Dave.
    <br>&nbsp;
    <br>&nbsp;</html>

    --------------3F00629D76F97211EDFA2FFB--

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    org:Foster-Miller, Inc.;Electrical and Electronic Systems Group
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    adr;quoted-printable:;;350 Second Avenue=0D=0A;Waltham;MA;02451-1196;USA
    fn:David Meeker, Ph.D.
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    - From: "McGee" <mcgee@mcmillan-mcgee.com>

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