A little question - Chile

Christophe Geuzaine Christophe.Geuzaine at ulg.ac.be
Fri Oct 27 15:32:20 CEST 2000

Hi Alejandro,

I took a look at your problems this morning. 

First mail

I see (for the moment) three issues that should be addressed:

1) I don't understand your boundary conditions on the vector potential.

2) I don't understand the characteristic lengths specified in the geo
file. (Maybe this is due to the buggy Windows version of Gmsh? I never
used this version, so I cannot say).

3) the global equations seem to heavily worsen the condition number of
the matrix in the complex case.


1') I tried to set the potential to zero on all the exterior boundary
(i.e. the transformer is enclosed in a shielding box --- which is
quite physical to my point of view). If the coils are in the air, then
you have to take infinity into account, and either use boundary
elements, or introduce a transformed region.

2') I changed the mesh a bit to get something more regular.

3') 1' and 2' seem to make the system easier to solve, but there is
still some conditionning problem. Before we find a better algorithm to
handle the global equations (I have a collegue working on this topic
for the moment), the only solution is to force some heavy
preconditionning of the linear system (ILUTP with e.g. 400 non zero
elements per line), and to use a long recursion algorithm for the
iterative solving (e.g. GMRES without restart).

The result of 1', 2' and 3' are contained in the small archive mail1.tgz
attached to this mail. Could you try to solve the problem with the
mesh I made (transormador.msh, in which the characteristic lenghts are
changed, as well as the definition of the physical line on which the
potential is imposed) and the solver parameters I introduced (in

Tell me how (if?) it works, and if the results make sense.

Second mail

The error is in the '91 paper. The guy (A. Nicolet) published the same
test case in his PhD, and the mesh was also displayed. I solved the
problem with this mesh (10 elements on the length of a winding -> set
pFle = 3.8e-2 and pFleM = 3.8e-2 in core.geo), and got approximately
the same (bad) results as in the paper. I attached a figure displaying
the phase of the current density along the first winding: the
difference shows clearly that you have to mesh more than it was done
in the article.

My best,

PS: You never annoy me with questions :-). When I don't answer to
e-mail in two or three days, it is likely that I am either away from
the office, or that my mailbox is so full that I easily forget to
answer to the oldest mails (so just send it back a week later as a
remainder... Shame on me!). BTW, in order for us to improve the user's
guide, you are welcome to send any corrections or additions to it: we
would like to change it from a "reference guide" to something more
close to the definition of a "user's guide", i.e. a guide which would
teach people to effectively use the software to solve their own

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