Re: [femm] Question in Axisym. Problems in Postprocessor

[dcm3c@xxxxxxx]

In a message dated 3/14/01 2:24:26 AM Eastern Standard Time, stsc_sh@xxxxxxxx 
writes:


> David:
>  
>    Thanks for reply soon. I use the (1) method at my origin work. But the 
> smoothing solution of B was not very good along the axi. The only diffrence 
> between you and me is the Gauss Point's location. It seems we always should 
> choose the centroid of a element as its Gauss Point. Is that right?


Yes, the method (1) from the last message gives the best results when 
evaluated at the centroid.  However, you still ought to be able to get 
reasonable values along  the axis if you are linearly interpolating A.  For 
example, you know that the radial field must be zero along the axis.  That 
just leaves the z-direction field.  The definition, in terms of A, is Bz = 
A[r]/r + A'[r].  If you are linearly interpolating A over the element next to 
zero, you can use the fact that A has to be zero at r=0 to get the result 
that the axial flux density is Bz=2 A'[r] along the axis.

Anyhow, to sort of distill the interpolation scheme used in the Henrotte 
paper, I've put up the document 
http://groups.yahoo.com/group/femm/files/interpolation.pdf  in the mailing 
list files section.

>    In function GetNodalB, I was not very clear now what method you used to 
> get nodal value when it is on interface? 
> Thank you. 


This is sort of an ugly little piece of code on my part.  The idea of this 
routine was to preserve the continuity of the normally directed B across an 
interface.  If you don't do any smoothing, you get this automatically--the 
normal flux across the interface is just the derivative of A along the 
interface for planar problems (or 1/(2 Pi r) times the derivative of flux in 
the direction along the interface for axisymmetric problems).  This routine 
assigns the normal portion of the flux density for the node points on the 
boundary on the basis of the slopes of the interface on either side of the 
node, rather than extrapolating B from the Gauss points of nearby nodes.  It 
gets the tangential part of B from interpolating from nearby nodes, because I 
found it hard to enforce continuity of tangential H at the boundary (it's 
only approximately enforced by first order triangles to begin with).  All of 
the messiness comes because not every interface is straight, i.e. arcs.  The 
code tries to figure out what should be considered to be a "smooth" 
interface, tries to figure out which direction should be the normal 
direction, and then enforces the "normal" derivative continuity.  If the 
angle is too steep, it decides that it's really a corner and doesn't try to 
smooth things out around it.

Honestly, I couldn't find a way to do it that truly satisfies me, and I 
couldn't find a good reference on superconvergence ("superconvergence" is the 
buzz word for smoothing in this type of problem) that deals with how to treat 
interfaces in a consistent way.  If anyone knows of a good reference, I'd 
really appreciate you posting it.

Dave.