ffc team mailing list archive

["Garth N. Wells" <gnw20@xxxxxxxxx>]

Kristian Oelgaard wrote:
> Quoting Anders Logg <logg@xxxxxxxxx>:
>
> > On Mon, Apr 28, 2008 at 08:25:53PM +0200, Kristian Oelgaard wrote:
> >
> > > # 2D plasticity, cases
> > > 1) 1st order elements, mesh(1000, 1000)
> > > 2) 2nd order elements, mesh(500, 500)
> > > 3) 3rd order elements, mesh(250, 250)
> > > 4) 4th order elements*, mesh(125, 125)
> > >
> > > *Note that because the bilinear form in this case is a 9th order form we
> > take
> > > the number of quadrature points equal to 5 when declaring the quadrature
> > element.
> >
> > Another optimization would be to reduce the number of quadrature
> > points. If your method is order p, then you only need to integrate the
> > form with quadrature exact for degree p polynomials. So in particular,
> > you don't necessarily need many quadrature points just because the
> > integrand has many factors.
>
> I don't quite follow. If the displacement field is 4th order, the gradient is
> 3rd order and the bilinear form is 9th order? And since 5 integration points
> can integrate 2*5-1 = 9th order polynomials exactly I would say we should use
> 5 integration points in each direction. This is also what the
> __init_quadrature() and __compute_degree() functions in monomialintegration.py
> will return.

I think the point Anders is making is that you don't need exact quadrature.

Garth

> Kristian
>  
> > A related optimization can be done for tensor representation by
> > projecting coefficients to a lower order space (like piecewise
> > constants).
> >
> > --
> > Anders
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>
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