Questions - Valparaíso - Chile

[Christophe Geuzaine]

Alejandro Angulo wrote:
> 
> Christophe:
> 
> For curiosity I have begun to solve a small
> axisymmetric problem that I send you in an attached
> file. This correspond a rectangular conductor with
> known current, surrounded of a ferromagnetic material
> of high permeability (infinite). Initially I forced
> one of the boundaries (SurfaceGeO) to have certain
> value of MVP (Drichlet Condition// Az=0!!) and the
> formulation ran without more problems. Then, I
> liberated this condition and I let that all boundaries
> of the model fulfill whith homogeneous Neumman
> conditions (this is a natural condition for this type
> of fomulation//that is to say null normal conmponent
> of magnetic field!!) and in thhis case the numeric
> solution (default solver) it began to oscillate and it
> didn't converge, reaching the maximum number of
> iterations. On the other hand, to verify my doubts, I
> used a commercial software (QuickField) to run the
> same model and in this didn't have bigger problems.
> Cristophe, can you revise this small problem, please,
> and to indicate me why it didn't work??
> 

You state the problems in terms of a potential, which is defined up to a
constant. If you don't specify any Dirichlet boundary conditions (i.e.
you don't specify any gauge), how should one choose between the members
of the equivalent class representing the potential?

A poor solution is to use an iterative method to solve the linear system
and to let the iterative method do the gauging (it should work, even if
the convergence may be more difficult). But the clean way to do it is to
fix the potential at least at one node.

Now, I don't know anything about the methods QuickField uses (if there
is some "intelligence" behind the algorithms, specifying additional
constraints, etc.). And by the way, what was the solution with
Quickfield like ? It should definitely not be the same as with a
Dirichlet BC. The two problems (with Dirichlet and Neumann BC) _are_
different.

-- 
Christophe Geuzaine

Tel: +32-(0)4-366.37.10    mailto:Christophe.Geuzaine at ulg.ac.be
Fax: +32-(0)4-366.29.10    http://www.geuz.org