Re: [femm] Asymmetry in FEMM solution...

[dcm3c@xxxxxxx]

In a message dated 10/11/00 4:10:24 PM Eastern Daylight Time, 
bshumm@xxxxxxxxx writes:

> Dear Dave and members of FEMM group,
> can anybody comment the fact, that the FEMM solution of axisymmetric 
> problem for symmetric about z=0 plane currents and environment may be 
> slightly asymmetric about the same plane. It may be seen for example 
> in the simplest case of Helmholtz coils (profile of |B| along line 
> near r,z=0 parallel to z-axis). This feature may baffle the attempt 
> of calculation of systems with large area of homogeneous magnetic 
> field (e.g. MRI magnets), where this asymmetry may exceed expected 
> inhomogeneity. Is there any way to exclude this effect? Thanks.
> Yours
> Boris A.Shumm

Even if your problem is perfectly symmetric, some asymmetry is introduced by 
the process of meshing--the mesh isn't exactly the same on one side of the 
problem as the other. You can lessen this effect by creating very fine 
meshes.

Alternatively, you can always enforce symmetry by only modeling part of the 
problem and using symmetry boundary conditions at the lines of symmetry. 
(Either apply A=0 for no flux normal to the line of symmetry, or don't apply 
any boundary condition at all--this implicitly enforces dA/dn=0 at the 
boundary for no flux tangential to the line of symmetry.)

Some improvement might be gained by increasing the precision required for a 
solution in the sparse matrix solver. You could represent the problem being 
solved in the standard A x = b form. The stopping criteria is currently 
hard-coded as
||A x - b|| / ||b|| < 1.e-08, where || || means taking the 2-norm. Another 
way of looking at is is that the RMS error divided by the RMS of b is < 
1.e-08. I sort of picked this arbitrarily, because it seemed like a good 
tradeoff between accuracy and taking forever to solve. This tolerance could 
be decreased by several orders of magnitude, if need be.

Dave.