ffc team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Sun, Aug 23, 2009 at 10:08:57PM +0200, Kristian Oelgaard wrote:
> Quoting Shawn Walker <walker@xxxxxxxxxxxxxxx>:
>
> >
> > On Sun, 23 Aug 2009, Peter Brune wrote:
> >
> > > I disagree!  I think that this in some sense returns us to the previous
> > objection with this method of
> > > defining the coordinates, in that it is a circular definition.  What I
> > recommend for standardizing this (and
> > > the completion of what I've done so far with it) is attaching the
> > coordinate function not to the cell, but to
> > > the measure on the integral.  It could be done using the existing metadata
> > functionality.  This would look
> > > something like:
> >
> > I may appear circular, but it would not be so in the implementation (i.e.
> > the FFC code).  If you want, you could think of this as overloading the
> > notation.
>
> I think Peter is right, although I did not follow the discussion closely the
> last time we had it. The implementation might not be circular, but the notation
> would look like it in the ufl file, which makes the metadata approach better.
> We just need to grab this information somewhere in FFC.
>
> > > coords = Function(iso_vector)
> > >
> > > a = dot(grad(u), grad(v)*dx(0, {"coordinate_function" : coords})
> > >
> > > or:
> > >
> > > coords = Function(iso_vector)
> > >
> > > a_t = dot(grad(u), grad(v))
> > >
> > > a = a_t*dx(0) + a_t*dx(1, {"coordinate_function" : coords})
> >
> > I am a little unclear on what this means.
> >
> > > Which would allow for both an isoparametric and affine parts of the domain
> > as separate integrals, but would
> > > allow the same test, trial, and coefficients to exist for both.  This would
> > allow one to treat curved
> > > boundaries and non-curved interiors, and is totally general -- if you want
> > part of your form to be radial or
> > > parabolic, you could do it.  This is basically what I'm doing right now,
> > only I've had to devise ways around
> > > the present system by first inverting the affine jacobian and then applying
> > the isoparametric jacobian.  I
> > > apply this with the form transformation machinery.  Also, the facet
> > integral would have to be rewritten to
> > > accomodate a full transformation rather than what is done now.  I've gotten
> > around this as well, but it took
> > > some work.  No offense, but it seems to need a rewrite anyways, especially
> > for the optimization. (I had it
> > > eat all my memory and die when I tried to turn on optimization on a facet
> > integral that involved a tensor.)
>
> A rewrite of the facet integral itself or the optimisations? Did you use the
> latest FFC version? If so can you send the form (or the part thereof) which
> kills your memory?
>
> >
> > I think you could have affine and non-affine with the other approach too,
> > but I guess having affine and non-affine interior facets would be a
> > problem.  But I'm not sure how the notation you listed above actually
> > deals with having affine and non-affine elements.  What exactly is the
> > iso_vector?
> >
> > Obviously, I am biased, but I think that having non-affine everywhere
> > would be easier to implement in FFC.
>
> Using affine mapping in one sub-domain and non-affine in another should be quite
> easy using the syntax Peter does above. That also take care of the 'variable
> quadrature rule' that you hint at below.
>
> That is basically what I did in that
> > demo code I sent out.  And the syntax that I propose would do that.  I
> > admit, it would be nice to have a variable quadrature rule over the
> > different entities based on whether or not they are affine.  You might be
> > able to do this with what I wrote below, but you would need some boolean
> > functions telling you what was affine and what was not, and I admit this
> > is wonky.  having non-affine everywhere is more expensive, but is not the
> > end of the world.
> >
> > - Shawn
> >
> > > I'm totally willing to sift through FFC to do this, but I sort of need to
> > know where to start.  Kristian, any
> > > hints?  (oh, and I still am looking at the quadrature stuff, but it's been
> > a busy summer for me here at KTH.
> > > :) )
>
> Well, if we go for the metadata approach, we should probably look for the
> 'coordinate_function' and set some flag that tells the transformers to generate
> transformations using this function. Perhaps we should give Anders a chance to
> throw in his two cents before doing anything drastically? That will give you a
> last chance to go out and enjoy the Swedish summer before it ends. :)

First, sorry for not weighing in on this earlier.

Second, I really like the form-based approach. The more we can
leverage UFL to do things the better.

So, if Peter thinks he knows how to handle this and if Shawn thinks it
will be enough for his purposes, then just go ahead and bring on the
patches. I'll try to be more responsive from now on.

Another thing to think about when we rethink the transformations/code
snippets is the possibility of extending to assembly over manifolds
(like a 2D surface embedded in R^3). We now make assumptions on the
domain being R^2.

Just one small thing. We're trying to put together a new release with
focus on parallelization so it might be good to hold off until we've
made that release so as not to delay it further.

--
Anders

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