[Getdp] Problem with description of magnetisation

[Patrick Dular]

Hi Peter,

For this kind of problem (static fields, no source currents), I think
the most efficient solution strategy is to use a scalar magnetic
potential. You can then compute the magnetization as a post-processing
quantity. In the linear case, this formulation is indeed the one given
in the demo file of the getdp distribution, i.e.

Formulation {
  { Name MagSta_phi ; Type FemEquation ;
    Quantity { 
      { Name phi ; Type Local ; NameOfSpace Hgrad_phi ; }
    }
    Equation {
      Galerkin { [ - mu[] * Dof{d phi} , {d phi} ] ;  
                 In Domain ; Jacobian JVol ; Integration I1 ; }
      Galerkin { [ - mu[] * hc[] , {d phi} ] ;  
                 In Domain_M ; Jacobian JVol ; Integration I1 ; }
    }
  }
}

where 'hc[]' is the volume source term (the coercitive magnetic field in
your magnets). This formulation is only valid if 'Domain' is
topologically trivial (no loops): for its construction, see
http://www.geuz.org/getdp/doc/slides/getdp-18.html,
http://www.geuz.org/getdp/doc/slides/getdp-25.html (and following), with
'j=0'. If the materials are weakly nonlinear, just write 'mu[{d phi}]'
instead of 'mu[]' in the equations, and use an 'IterativeLoop' in the
resolution. If the materials are strongly nonlinear, you may want to use
a Newton method, which requires the definition of an additional term in
the formulation. Tell me if this is the case: I'll show you how to
construct it.

Christophe



pf231 at cam.ac.uk wrote:
> 
> Dear all,
> 
> Thank you, first of all, to Christophe and Patrick for the brilliant
> getdp program.
> 
> I am presently working on a 3D FEM simulation of the transition region
> from a permanent magnetic hexapole field to a dipole field. Being no
> expert in FEM simulations at all I find myself in a problem, where I
> need some help, which I hope you can provide me with:
> 
> I want to describe the system in a vector potential approach with the
> edge finite elements with the tree gauging, that you sketched in the
> manual. The problem comes in, when I try to describe the magnetisation.
> 
> Which function space can I use for it? A vector field didn?t work,
> because I couldn?t define a curl on it (curl (magnetisation)=0), but
> otherwise I don?t know how to get it into the Galerkin equation (if I
> use it as a constant) or to define it properly (if I use a 1form space
> for the magnetisation).
> 
> If you could give me a direction to solve the problem, I would be
> extremely grateful to you.
> 
> Thank you very much in advance, best regards
> 
> Peter Fouquet
> 
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-- 
Christophe Geuzaine

Tel: 32 (0) 4 366 37 10    http://geuz.org
Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be