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# Re: number of points in material defintion

- To: femm@yahoogroups.com
- Subject: Re: number of points in material defintion
- From: "David Meeker <dmeeker@ieee.org>" <dmeeker@ieee.org>
- Date: Tue, 04 Feb 2003 14:47:14 -0000
- In-reply-to: <b1o3al+1rgf@eGroups.com>
- User-agent: eGroups-EW/0.82

    --- In femm@yahoogroups.com, "Michael Salloker
    <michael.salloker@f...>" <michael.salloker@f...> wrote:
    > Hello,
    >
    > I wonder how many points un B-H-curve are necessary to get a good
    > description of a ferromagnetic material.
    >
    > I found out, that increasing the number of points also increase the
    > speed of the calculation, so its necessary to find a sufficient large
    > number of data points.
    >
    > So imagine I have a material with a saturation of about 1T, i could
    > do a spacing of 0.1 T, or 0.05T aso. In general I believe its better
    > to make aquidistant points for B and for H, due the nonlinearity.
    >
    > Whats is the experts opnion?
    >
    > Thanks
    >
    > Michael

    The program interpolates the entered points using cubic splines.
    Cubic splines are twice continuously differentiable, so you don't need
    an excessive number of points to get a smooth BH curve.

    Generally, it is good to have more points around the "knee" of the BH
    curve. If there are not enough points around the knee, the program
    can't fit a monotonically increasing BH curve through the points. The
    program then smooths the data points repeatedly until the fit becomes
    monotonic--the cost for this smoothness is that the curve doesn't pass
    exactly through the defined points.

    If you push the "plot BH curve" button on the BH point entry dialog,
    the program plots up the fitted curve, along with the data points. If
    the program had to smooth, the fitted curve doesn't exactly pass
    through the data points. You can add more points (typically around
    the knee) to get things so that the program doesn't have to do any
    smoothing--although the smoothed curve that doesn't exactly pass
    through the defined points might be good enough for your purposes
    without having to add in extra points.

    Another consideration is that you'd typically want to make sure that
    you extend out the BH curve far enough so that you aren't
    extrapolating the BH curve at any of the points in your solution.

    Typically, I try to make the points somewhat evenly spaced in sort of
    a line integral sense. For example, if dB and dH are the differences
    in B and H respectively between successive points on the BH curve, and
    Bmax and Hmax are the last point on the curve, I try to make:
    sqrt((dB/Bmax)^2 + (dH/Hmax)^2)
    be sort of constant. However, this is just sort of a rule of thumb.

    Typically, most of the points in the materials library have about 15
    or so points.

    Dave.
    --
    David Meeker
    http://femm.berlios.de/dmeeker

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- References:
  - number of points in material defintion
    - From: "Michael Salloker <michael.salloker@fh-joanneum.at>" <michael.salloker@fh-joanneum.at>

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