dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Mon, Jan 22, 2007 at 11:37:47AM +0100, Anders Logg wrote:
> On Sun, Jan 21, 2007 at 10:44:11PM +0100, Johan Jansson wrote:
> > On Sun, Jan 21, 2007 at 06:11:03PM -0300, Pablo De Napoli wrote:
> > > Hi!
> > > 
> > > My name is Pablo De Nápoli, I work at the Department of  Mathematics atBuenos
> > > Aires University, Argentina.
> > > 
> > > I'm new to Dolfin, and I'm planning to use for some numerical experiments in
> > > my research. I think it is a very interesting software specially for
> > > the close to the
> > > mathematical-thinking way of representing the PDEs in weak formulation.
> > > 
> > 
> > ...
> > 
> > > Could you please explain me what is wrong in this program?
> > > User-defined functions can't be plotted? (exported to files?)
> > > 
> > 
> > Hi Pablo,
> > 
> > Yes, user-defined functions cannot be directly plotted/exported to
> > file. You need to project the function to a finite element space to do
> > that. I've modified your program to achieve that:
> > 
> > #include <dolfin.h>
> > #include "Projection.h"
> > 
> > using namespace dolfin;
> > 
> > int main()
> > {
> >   class Myfunction : public Function
> >   {
> >     real eval(const Point& p, unsigned int i)
> >     {
> >       real x= p.x();
> >       real y= p.y();
> >       return (x+y);
> >     }
> >   };
> > 
> > 
> >   UnitSquare mesh(16, 16);
> > 
> >   Myfunction f;
> >   Projection::BilinearForm a;
> >   Projection::LinearForm L(f);
> > 
> >   LinearPDE pde(a, L, mesh);
> > 
> >   Function F;
> >   pde.solve(F);
> > 
> >   File file("F.pvd");
> >   file << F;
> > 
> >   return 0;
> > }
> > 
> > with the form "Projection.form":
> > 
> > # Compile this form with FFC: ffc Projection.form.
> > 
> > element = FiniteElement("Lagrange", "triangle", 1)
> > 
> > v = TestFunction(element)
> > U = TrialFunction(element)
> > f = Function(element)
> > 
> > a = v * U * dx
> > L = v * f * dx
> > 
> > There is experimental functionality to simplify the computation of
> > projections, since it's so fundamental, but it's not quite stable yet.
> > 
> > Export of user-defined functions could be implemented by automatically
> > performing a projection as above.
> > 
> > > By the way, I think that the code in section 4.3.2 Dolfin's manual
> > > (User-defined functions) is not correct
> > > 
> > > for example Instead of
> > > 
> > > class Source : public Function
> > > {
> > >   real eval(const Point& p, unsigned int i)
> > >   {
> > >     return x*y*sin(z / DOLFIN_PI);
> > >   }
> > > };
> > > 
> > > (this form of the code didn't work for me)
> > > it should be
> > > 
> > > class Source : public Function
> > > {
> > >   real eval(const Point& p, unsigned int i)
> > >   {
> > >     return p.x()*p.y()*sin(p.z() / DOLFIN_PI);
> > >   }
> > > };
> > > 
> > > and likewise in the other examples in that section....
> > 
> > You're right, this is because the mesh representation has recently
> > changed. The documentation should be updated more frequently, but
> > since fundamental interfaces are still being implemented/improved,
> > that is given higher priority.
> 
> This will improve in the near future. The linear algebra interface
> stabilized during the summer, the new mesh library is now in firm
> place and the assembly/form evaluation will soon be in place (and stay
> fixed).
> 
> After that, the interfaces will be remain mostly constant and we will
> be able to write a useful manual.
> 
> /Anders

Another comment concerning plotting: Ola Skavhaug has developed a
small and simple VTK-based plot library that can be used for simple
plotting of DOLFIN functions (not yet user-defined). When this new
library is in place, you'll be able to do

    u = Function(...)
    plot(u)

from PyDOLFIN.

/Anders