[dune-pdelab] periodic boundary conditions

[Christian Engwer]

Hi!

first you have to settle the question of the grid. I don't have a
complete overview of the support of periodic boundaries of the
different grid managers.

I know:
- YaspGrid handles what you want, but without inclusions
- UG does have some kind of periodic support, but I don't know what
  exactly is supported and you can't use easily fromm DUNE [patches
  wellcome ;-)]
- Alugrid from 1.23 on support periodic boundaries in 3D

Depending on the grid you are using the periodicity is implemented
similar to parallel coupling, which uses domain decomposition with
overlap or ghosts. In this case you should use the periodic
constraints. If the grid implements periodicity as periodicity in the
topology of the grid, you don't have to change anything (not sure if
any grid supports this).

The last option is implement periodictity in PDELab without support of
the grid. You should the write your own constraints-assembler
local-operator, which adds dirichlet constraints on one side. There is
no real tutorial on this. You will have to dive into it...

Christian

> I need a fully periodic cube: left-right, top-bottom in 2D,
> and additionally front-back in 3D.
> The cube has an arbitrarily shaped inclusion(like a circle or a sphere) inside,
> with Dirichlet b.c.
> I was looking at section 8.4 of the tutorial explaining constraints
> for Dirichlet b.c.,
> but the transformation matrix there is local, when I need the global one for the
> periodic b.c.
> Can you point me to the source file that does what you described above?
> 
> regards,
> Oleh
> 
> 
> 
> 2011/10/31 Christian Engwer <christian.engwer at uni-muenster.de>:
> > Dear Oleh,
> >
> >> I need to implement periodic boundary conditions for a transport problem.
> >> Google shows that there's no such functionality in DUNE at the moment.
> >> Perhaps someone can give me some pointers or suggestions on how
> >> to implement periodic b.c. in a straightforward way.
> >
> > it depends on which BC you need.
> >
> > Straight forward: You have a mesh like this:
> >
> > o-x-x-x-o
> > | | | | |
> > o-x-x-x-o
> > | | | | |
> > o-x-x-x-o
> >
> > where the 'o' nodes are associated with each other. This kind of mesh
> > is available with yaspgrid. It is implemented as a periodic mesh with
> > overlap on the left and right side.
> >
> > If you need something more general it will get tricky and you should
> > explain in detail what you want to achieve.
> >
> > Cheers
> > Christian
> >
> >
>