On Tue, 26 Aug 2014 09:50:23 +0100
"Garth N. Wells" <[email protected]> wrote:
> To summarise this thread, it seems we need to introduce the concept
> of an 'Expression' that can be evaluated at arbitrary points. It
> should not be a Quadrature{Element/Function} because the proposed
> object could be used in different forms with different evaluation
> points. The follow-on on issue is then how a 'point-wise' expression
> should be treated in forms. We could estimate the quadrature scheme
> when test/trial functions are present, and in the case of functionals
> throw an error if the user doesn't supply the quadrature degree.
There's no principal difference regarding rank of the form. Consider
f = PointwiseExpression(eval_formula)
u, v = TrialFunction(V), TestFunction(V)
a = f*u*v*dx
L = f*v*dx
F = f*dx
Still, you need to know what is the polynomial degree of f to have
exact quadrature of any of these forms. Ignoring non-zero degree of f
(which seems to me you do suggest for a and L) means that you're
underintegrating any of those three forms. This is analogical to
integrating F with scheme of order zero. I don't see any good reason
why having distinct behaviour based on rank of the respective form.
Jan
>
> If this is the consensus, we can add an issue(s) to Bitbucket. Please
> reply with feedback.
>
> Garth
>
>
> On Fri, 15 Aug, 2014 at 9:27 AM, Martin Sandve Alnæs
> <[email protected]> wrote:
> > On 14 August 2014 11:09, Martin Sandve Alnæs <[email protected]>
> > wrote:
> >> On 14 August 2014 10:38, Garth N. Wells <[email protected]> wrote:
> >>> I favour (a) explicit provision of the element/function space; or
> >>> (b) evaluation at quadrature points with errors for cases where
> >>> no data is available for deciding on a sensible quadrature
> >>> scheme. Using quadrature points would fix some other awkward
> >>> issues, like specifying boundary conditions on polygon faces
> >>> which 'creep' around corners is subdomains are not marked.
> >>
> >>
> >> I agree with both (a) and (b).
> >
> > I see I was a bit quick there.
> >
> > I favour evaluation at quadrature points for cases where no
> > element/function space is provided, combined with making the choice
> > of quadrature degree/scheme easier accessible with dx(degree=3)
> > notation. Maybe we can add in a "Warning: automatic selection of
> > integration degree 3, this may be inexact.".
> >
> > The quadrature degree estimation is just that: an _estimation_. It
> > is not exact for any non-polynomial expressions. If we want to
> > throw an error when the degree for exact integration cannot be
> > determined, that is a partially separate issue from this one, and
> > it will break a lot of programs. If we want integration involving
> > any Expression without an element to be guaranteed exact, we will
> > need to require the integration degree to be set explicitly. This
> > will probably break every single dolfin demo.
> >
> > Martin
>
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