ffc team mailing list archive

[Kristian Oelgaard <k.b.oelgaard@xxxxxxxxxx>]

Quoting Anders Logg <logg@xxxxxxxxx>:

> On Mon, Nov 23, 2009 at 08:50:14AM +0100, Kristian Oelgaard wrote:
> > Quoting Anders Logg <logg@xxxxxxxxx>:
> >
> > > On Mon, Nov 23, 2009 at 07:39:24AM +0100, Kristian Oelgaard wrote:
> > > > Quoting Anders Logg <logg@xxxxxxxxx>:
> > > >
> > > > > On Tue, Nov 17, 2009 at 09:28:23PM +0000, Garth N. Wells wrote:
> > > > > >
> > > > > >
> > > > > > Anders Logg wrote:
> > > > > > >I've added support in UFL and FFC for letting quadrature degree be
> > > > > > >None for a quadrature element.
> > > > > > >
> > > > > > >This lets the form compiler choose the quadrature. What currently
> > > > > > >happens is that the degree is counted as 1
> > > > > >
> > > > > > Polynomial degree or 'quadrature degree' (whatever that is)?
> > > > > >
> > > > > > (default value controllable
> > > > > > >from the form compiler) and the summed with other functions
> > > > > > >multiplying the coefficient.
> > > > > > >
> > > > > > >  L = v*f*dx
> > > > > > >
> > > > > > >If v is P2, then the total degree will be 2 + 1 = 3, which means
> the
> > > > > > >quadrature degree chosen by FFC is 3 for that integral and so also
> > > > > > >for the element for f.
> > > >
> > > > Sounds reasonable.
> > > >
> > > > > > >Then there seems to be some confusion about the difference between
> > > > > > >quadrature order and degree. At least I'm confused.
> > > > > >
> > > > > > Me too.
> > > >
> > > > It should be the same thing, but we could sort out the naming to avoid
> > > > confusion. I think this originates from Martin using 'polynomial
> degree'
> > > and I
> > > > used 'polynomial order' when first implementing this.
> > >
> > > I think degree is better. Quadrature order q can mean either that the
> error
> > > converges as h^q and polynomials of degree q - 1 are integrated
> > > exactly, or it can (in the case of Gauss quadrature) that it
> > > integrates polynomials of degree 2q - 1 exactly.
> > >
> > > We can define degree of a quadrature rule to be the polynomial degree
> > > it integrates exactly. Then there's no confusion.
> >
> > That's how I defined it, only I used 'order' instead of 'degree'.
> > But let's do a search and replace to change order to degree.
>
> ok.
>
> > > The problem is the following though. Should the quadrature rule of an
> > > element be an appropriate rule for the entire integrand, or should it
> > > be the polynomial degree approximation of the coefficient?
> > >
> > > Currently, if one has w being defined on a quadrature element of
> > > degree q, then the form
> > >
> > >   w^n * dx
> > >
> > > gets a total degree of n * q and FFC adjusts the quadrature rule to
> > > that total degree.
> >
> > If I compute some field e.g., the strain from the displacement field at
> > quadrature points and then pass it as a coefficient to some other form,
> then
> > the order has to stay the same otherwise this get screwed up.
> > So if the order is set by the user, it shouldn't change, but if it is set
> to
> > None FFC should set it equal to the order needed to evaluate the integrand
> > exactly.
>
> Sounds good, with the following modification:
>
>   if degree is None:
>     if quadrature_degree(form) is None:
>       degree = polynomial_degree(form)
>     else:
>       degree = quadrature_degree(form)
>
> quadrature_degree is the degree of any other quadrature elements in
> the form (which needs to be the same for all if specified).
>
> polynomial_degree is the total polynomial degree of the form.

OK, sounds good.

Kristian

> --
> Anders
>