dolfin team mailing list archive

["Matthew Knepley" <knepley@xxxxxxxxx>]

On 7/10/07, Martin Sandve Alnæs <martinal@xxxxxxxxx> wrote:
> 2007/7/10, Matthew Knepley <knepley@xxxxxxxxx>:
> > On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
> > >
> > >
> > > Matthew Knepley wrote:
> > > > On 7/9/07, Anders Logg <logg@xxxxxxxxx> wrote:
> > > >> It looks to me like the (quad) cell which first has vertices 1-2-5-4
> > > >> after the surgery has vertices 1-(0)-(2)-3. What are then the
> > > >
> > > > Yes.
> > > >
> > > >> coordinates of vertices (0) and (2)? Same as for 0 and 2, or same as
> > > >> original 2 and 5?
> > > >
> > > > Same as (0) and (2) since no other vertices actually exist in the mesh.
> > > > Those are vertices 0 and 2. I put them in parens to emphasize that I
> > > > was writing them twice, but they exist only once. Next time I will just
> > > > write the Sieves. Much clearer :)
> > > >
> > > >   Matt
> > >
> > > It still doesn't make sense to me, but maybe I'm just getting tired...
> > >
> > > If the coordinates of (0) and (2) are the same as those of 0 and 2,
> > > won't we get the wrong geometry for the cells on the boundary? Imagine
> > > having a much finer grid. Then the cells on the right boundary will
> > > stretch all the way back to touch the left boundary.
> >
> > Yes, but that is why I put in the explanation for calculation of J. With the
> > exception of coordinate functions (which we can talk about after this),
> > you only need J or functions of it. Now, the Jacobian only depends on
> > coordinate differences. So you just need something like
> >
> >   dx = (x_1 - x_0) mod L
> >
> > where L is the periodic length.
> >
> >   Matt
>
> This sounds restricted to a small set of simple geometries?

There is a big difference between topologies and geometries :) If you have
a truly periodic geometry WITHOUT handles, then it looks like R^n x T^{n-k}.
(Notice I accidentally wrote S^{n-k} last time which is incorrect) Of course
you can have a more complicated fundamental group, but people
just usually do not setup periodic problems like that.

> Just as a side-note, we recently had a tutorial for Star-CD (a
> commercial closed source fluid flow application), and there you could
> designate two boundaries of the mesh a cyclic even if they didn't
> match completely. It would then do interpolation between arbitrary
> discretizations of the cyclic boundaries. I guess the geometries had
> to be rougly the same, or it wouldn't make much sense anyway.

Yes, so topologically its the same as I was proposing. They just do it in
an inelegant way in my opinion. I would first start with the cell complex
that captures the topology, which would be periodic and structured like
I propose. Then for accuracy considerations this wold be refined IN a
periodic sense (probably using Anders new stuff). This is why I have never
liked Star-CD. They put a lot of hard work into the wrong ideas.

> You already have the interpolation between different discretizations,
> right? So this could be possible to do.

Sure.

 Thanks,

    Matt

> Martin
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What most experimenters take for granted before they begin their
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