[Getdp] basic permant magnet question - please help

[Olivier Castany]

>        Equation {
>                     Galerkin { [nu[] * Dof{ Curl a}, {Curl a}]; In Domain; 
> Jacobian JVol; Integration I1; }
>                     Galerkin { [hc[], {Curl a}; In Domain_M; Jacobian 
> JVol; Integration I1;}
>         }
> 
> How does {hc[], {Curl a}} come into the equation? I believe that hc is 
> Coercitivity of the magnet?


The relation between H and B in a magnet is complicated. If the magnet 
is used in a narrow enough (H,B) domain around a working point, the 
relation can be assumed to be linear.

Examples of working points are : (H,B) = (-Hc,0), (0,Br) or whatever 
fits the physical situation.

In the case of a working point (H,B) = (-Hc,0), the relation in the 
magnet is linearized as : B = mu * (H + Hc)

(outside the volume of the magnet, mu is different and there is no Hc)

The Maxwell equation without free current is : rot(H) = 0
which implies : rot(B/mu - Hc) = 0

The divergence-free field B is written as : B = rot(A). 
If A is a solution, it satisfies :

\int_Domain rot(rot(A)/mu - Hc) * A' = 0, for all A' 

Boundary conditions must be taken into account. Suppose the border of 
Domain is made of two parts S1 and S2 with the following boundary 
conditions :
- values of A are imposed on S1
- H // n on S2 (n = normal to S2)  

Let us call AA the set of all possible A' with vanishing value on S1. 
>From the previous equation, we deduce :

\int_Domain (rot(A)/mu - Hc) * rot(A') = 0, for all A' in AA

(the relation "rot(H) * A' = H * rot(A') + div(H x A')" has been used)

The two terms are written in GetDP in the following way :

Galerkin { [ 1/mu[] * Dof{d A} , {d A} ] ; ... }
Galerkin { [ - Hc[] , {d A} ] ; ... }

-- 
O.C.