[Getdp] Periodic Boundary Conditions

[Christophe Geuzaine]

Francisco Jorge Santana Martín wrote:
> 
>  Dear Christophe Geuzaine:
> 
>   Thanks very much for your quickly answer we want to say with 
> "constraint of binary type" this other "Periodic Boundary Conditions".
>   These are our files of test.
>

<snip>

> 
>   Constraint {
> 
>   { Name periodic;Type Link ;//???????? here is our problem.
> 
>       Case {
>        { Region Line_Left ;}//???????????  here is our problem.
>        { Region Line_Right; }//????????????  here is our problem.
> 
>       }
>     }
> 

The idea is the following: the periodic boundary condition links the
degrees of freedom in the constrained region with the degrees of freedom
in a "reference" region, with some coefficient.

In your example, this would be something like this:

{ Name periodic;
   Case {
     { Region Line_Left; Type Link ; RegionRef Line_Right;
       Coefficient -1; Function Vector[$X+2*Pi,$Y,$Z] ;
     }
   }
}

where the constrained region is Line_Left, the reference region is
Line_Right and the coefficient is -1.

For this type of constraint to work in getdp, one needs to specify
explicitly the geometrical mapping between the constrained region and
the reference region. This is done with the "Function" above, which
translates the geometrical nodes in Line_Left by "2*Pi" along the
X-axis, so that they correspond with the nodes in Line_Right.

Beware that for this mapping to work, the meshes of Line_Left and
Line_Right *must* be identical.

I will try to put a complete example in the wiki when I have some spare
time.

Take care,

Christophe

-- 
Christophe Geuzaine
Applied and Computational Mathematics, Caltech
geuzaine at acm.caltech.edu - http://geuz.org