Re: [femm] about Mixed boundary condition

[David Meeker <dmeeker@xxxxxxxx>]

Jan Zimon wrote:

> HI !
>
> Could anybody help me find some information about Mixed 
> boundary condition in Axi-symmetrical problems (i'm beginner). 
> Where can i find any informations about (*.pdf or webside)? 
> Is it true condition
> A(r,z)= SIGMA[m=1..oo]((a_m/r^m)cos(mz+alpha_m)?
> Thank you for any help.
>
> Jan
I guess that what you are really asking for is a reference on the 
Axisymmetric case of the Asymptotic Boundary Condition. The form of the 
general solution for vector potential A isn't the same in the 
axisymmetric case as it is in the planar case, but everything comes out 
in the wash such that you enter in the same 1/(R*mu_o) value in the "c0 
coefficient" box of the dialog, where R is the radius of a circular (or 
half circle, for axisymmetric) domain.

A reference for this would be:

S. Gratkowski, L. Pichon, and H. Gajan, "Asymptotic boundary conditions 
for open boundaries of axisymmetric magnetostatic finite-element 
models," IEEE Transactions on Magnetics, 38(2):469-472, March 2002.

They derive the boundary condition as dA/dR + 2 A/R = 0, where R is 
distance from the origin (i.e. working in spherical coordinates). If I 
remember correctly, there was sort of a subtle trick to converting it to 
the boundary condition form that is implemented in FEMM. The boundary 
condition that the program implements is (1/u)Grad(A).n + c0 A + c1 = 0. 
In the axisymmetric case, Grad(A) = A/R + dA/dR, so that to get the 
dA/dR + 2 A/R = 0 form, you have to pick c0=1/(u*R) and c1=0. Every 
time I run across that paper, I think "where did the 2 go?" and end up 
running through this same thought process again....

Dave.

--
David Meeker
dmeeker@xxxxxxxx
http://femm.berlios.de/dmeeker