Christophe Geuzaine Christophe.Geuzaine at
Thu May 4 10:32:10 CEST 2000

"robin.cornelius" wrote:
> I am currently experimenting with GetDP in order to use it on some magnetics
> problems I am doing some research into. I was hoping if you could give some
> advice on using GetDP for the problem I will now describe:-
> I am involved in pulsed field magnotometry, that is we expose samples of
> magnets to a sinusoidal pulse that is of high enough field strength to
> ensure the magnet will completely saturate during both the positive and
> negative parts of the pulse. (We achieve this using capacitor banks
> discharging in to large coils). We measure the applied field and also deduce
> the M-field of the magnet to produce MH and BH plots.
> I am currently trying to simulate this process so we can look at the effects
> of eddy currents with in the magnet.
> The problem could initially be looked at in 2D. I do however wish to use
> transient analysis (not time harmonic);
> The domains would consist of Air with some source conductors with in it and
> The Permanent Magnet.
> 1.
> My first main question is how to introduce a source current density that is
> time dependent. I have tried adjusting the examples but do not seem to find
> a way of making it work. In your examples you use the source current density
> as a constraint in the inductor region, but it doesn't seem possible that
> the constraint can be time dependent. How can I get a time varying source ?

Several possibilities exists. The simplest, if you use a constraint for
imposing the current density, is to add a modulation to the constraint
by adding a "TimeFunction" in the constraint field. For example,

{ Name Current_2D ;
  Case {
    { Region Ind ; Value 1.e3 ; TimeFunction
Exp[-$Time^2]*Cos[50*$Time]; }

This will multiply the value of the constraint by the approriate time
function at each time step. The time function is just another function,
and it could more more elegant to define it in the Function field:

  MyTimeFct[] = Exp[-$Time^2]*Cos[50*$Time] ;
  MyValue = 1.e3 ;

{ Name Current_2D ;
  Case {
    { Region Ind ; Value MyValue ; TimeFunction MyTimeFct[]; }

Of course, you have to consider a time integration scheme in the
Resolution field. For a parabolic problem (eddy currents), a theta time
scheme is the appropriate choice.

> I have seen a situation in a commercial FEA package ( using magnetic scalar
> potential formulation) where a boundry condition was set to be time step
> dependent, so at each time step the magnetic scalar potential was calculated
> for the boundary thus producing a homogenous field. If this was possible it
> would be good but I would really like to be able to set time dependent
> current densities.
> 2.
> I need to be able to model non linear materials. I have looked at using M =
> Atan (B)  and mu = differential of (Atan(B) models of material
> characteristics. I have introduced this for mu in the time domain example
> given, but I would like to know if it is possible to use a different mu[]
> for different time steps so that I could use mu[a] for 0 < time <0.25 ,
> mu[b] for 0.25 <time <0.75 and mu[a] for 0.75<time<1. (Where time varies
> from 0-1). The reason I would like to do this is so I can use two Atan
> models ie Atan(x+c) and Atan(x-c)  so that hysterysis of the material is
> taken into account.

This is possible, but tricky: you can duplicate the equation terms with
appropriate tests. That is, multiply the first duplicated term by
($Time<0.25?1:0)*mu[{a}], the second by (($Time>0.25 &&
$Time<0.75)?1:0)*mu[{d a}]), etc. 

> 3. I would like to introduce into the formulation the ability to have eddy
> currents in the permanent Magnet and have the M field of the permanent
> Magnet included in the simulation as well. Do you have any advice for doing
> this .

You really have to write the eddy current formulation, defining your set
of variables from the beginning. A good reading is Alain Bossavit's

  author =	 "A. Bossavit",
  title =	 "Computational Electromagnetism. {V}ariational
                  Formulations, Edge Elements, Complementarity",
  publisher =	 "Academic Press",
  year =	 1998

My best,

Christophe Geuzaine

Tel: +32-(0)4-366.37.10    mailto:Christophe.Geuzaine at
Fax: +32-(0)4-366.29.10