dolfin team mailing list archive

[kent-and@xxxxxxxxx]

> 2008/8/20 Anders Logg <logg@xxxxxxxxx>:
>> On Wed, Aug 20, 2008 at 08:43:08AM -0600, Ostien, Jakob T wrote:
>>> Hi,
>>>
>>> I need to be able to assemble an active set of integration points.
>>> Essentially, to determine the set I loop over cells and then loop again
>>> over the integration points in the cell and determine if that
>>> integration point is active with some criteria.  Then I'd like to be
>>> able to assemble that set.
>>>
>>> This is a problem because currently the element_tensor does not break
>>> down into integration points, and I need to take derivatives, so the
>>> QuadratureElement in FFC is also ruled out.  I suppose I could
>>> calculate derivatives and then project on the QuadratureElement, but
>>> that seems sort of unclean.
>>>
>>> It seems like the recent discussion about integrating at a point (on
>>> the UFC list) might help me out here.
>>>
>>> Any other thoughts on how I might go about this?
>>>
>>> Jake
>>
>> I don't know yet. I'm thinking about how much of this should go into
>> the compiler and how much should be left to the user.
>>
>> We're working on similar things (and I know Garth is too). I think a
>> common denominator would at least be to be able to evaluate a form at
>> a given point.
>>
>> I like Kent's suggestion earlier about adding a new UFC class to go
>> along with the other three integral classes, something like
>>
>>  point_integral
>>
>> with tabulate_tensor taking the coordinates for a point as additional
>> input.
>>
>> --
>> Anders
>
> I liked your version with adding a new function to each *_integral class
> better.
> The reason is that each *_integral object will correspond to one
> foo*dx(i) or bar*ds(j)
> in the form definition, and each *_integral object will be able to
> compute both an
> integral over some cell and the corresponding integrand.
>
> Although a separate point_integral might make sense for something I
> don't know about,
> matching them to corresponding cell_integral, exterior_facet_integral
> and interior_facet_integral
> objects will become messy.
>
> --
> Martin

One may consider point evaluation also as a form, that was my point.

There is an advantage with adding a new function to the classes in the sense
that the operators and functions make sense in certain places.
Eg. jump can be evaluated on points in the interior of a facet whereas it
should not be used on the interior of a cell (note that the jump function
does not
have the same meaning in eg. a vertex). This coincide (of course) with the
the standard usage of dx, ds, and dS. Although with dx, ds, dS one knows that
eg jump is not evaluated at vertices because of the choosen quadrature
points.

An advantage of having a separate form object and a separate dx-like
symbol in
the form language, say dp or delta, is that one may then define forms that
are not
based on the dx, ds, and dS forms. Put in another way, one can eg. define
functions
in this way;

f = u*sin(x)*dp

(although dp does not look nice and I don't have any good suggestion).

Kent