ffc team mailing list archive

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

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.

Kristian
 
> A related optimization can be done for tensor representation by
> projecting coefficients to a lower order space (like piecewise
> constants).
> 
> -- 
> Anders
> _______________________________________________
> FFC-dev mailing list
> FFC-dev@xxxxxxxxxx
> http://www.fenics.org/mailman/listinfo/ffc-dev
>