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Re: [femm] eddy-curr in a tube
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.
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<p>McGee wrote:
<blockquote TYPE=CITE> <font color="#0000FF"><font size=-1>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.</font></font> <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.
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.
<p>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.
<p>Dave.
<br>
<br> </html>
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