dolfin team mailing list archive

[mspieg <mspieg@xxxxxxxxxxxxxxxxx>]

On Jun 23, 2008, at 6:13 AM, Kristian Oelgaard wrote:

> Quoting mspieg <mspieg@xxxxxxxxxxxxxxxxx>:
>
> > On Jun 21, 2008, at 9:50 AM, Kristian Oelgaard wrote:
> >
> > > Quoting mspieg <mspieg@xxxxxxxxxxxxxxxxx>:
> > >
> > > > Hi all,
> > > >      does anyone have an example  of how to access the coordinates
> > > > and set the Dofs (quadrature points) for a user defined Function
> > > > defined with a Quadrature element?  From what I can glean from the
> > > > documentation, this should be possible, but I can't quite figure  
> > > > out
> > > > how to do it.
> > >
> > > To set the values of you user defined function, just overload the
> > > eval()
> > > function like you would for a function defined on a 'normal'  
> > > element.
> > > When the function is being integrated in the form it will be
> > > evaluated at
> > > quadrature points, meaning that whatever coordinates are entering
> > > eval() (the x
> > > argument) will be the location of the quadrature point (the 'dof').
> >
> > Thanks Kristian,
> >
> > I figured out how to do this and it all works...the only issue is
> > that this function is a source term in a time-dependent non-linear
> > solve that is rather expensive to compute.  Right now it is being
> > evaluated every time the residual vector is being assembled, but
> > really only needs to be calculated once per time step.
>
> So what you have is (in sloppy DOLFIN syntax):

---
snippet deleted
---------

yep...pretty much

> > I'm curious to know if there is a straightforward way to evaluate it
> > once (at the quadrature points), outside of the form assembly, and
> > then just pass the tabulated function to the form within the non-
> > linear solve.  (I'm getting excellent quadratic convergence in the
> > newton solve, but this would speed things up by about a factor of  
> > 3-4).
>
> Happy to hear that it converges.
>
> I see too ways to do what you want (someone else might see better  
> ways?):
>
> Create a discrete function and for each time step compute the  
> entries of the
> underlying vector:
>
>   Vector vec;
>   Function F_ex(mesh, vec, form);
>
>   loop time
>   {
>     // evaluate function according to the definition
>     evaluate_complex_function(vec);
>
>     newton_solver.solve(nonlinear_problem, x);
>   }


This is what I wanted to do initially, but requires that I have  
access to the coordinates of the quadrature points.

I think I'll start with your second suggestion as that should be easy  
enough to implement

thanks
marc

	
	
> Or you can let FFC/DOLFIN handle things for you by defining a  
> simple form and
> let the assembler take care of things for you
>
> In FFC:
>   L = v*f*dx # Functions defined on QuadratureElement
>
> and in main.cpp:
>
>   Vector vec;
>   Function F_simple(mesh, vec, form);
>   ExpensiveFunction F_ex;
>   SimpleFormLinearForm L_simple(F_ex);
>
>   loop time
>   {
>     // The assembler will evaluate the expensive function once for  
> each time
>     // step and store the values in the simple function
>     assemble(vec, L_simple, mesh);
>
>     newton_solver.solve(nonlinear_problem, x);
>   }
>
>   Note: Your RHS form in nonlinear problem should use the F_simple  
> function
>   which is evaluated once per time step.
>
>   I think this should work.
>
> Kristian
>
>
> > All help greatly appreciated
> > cheers
> > marc
> > > >
> >
> >
> > > > ----------------------------------------------------
> > > > Marc Spiegelman
> > > > Lamont-Doherty Earth Observatory
> > > > Dept. of Applied Physics/Applied Math
> > > > Columbia University
> > > > http://www.ldeo.columbia.edu/~mspieg
> > > > tel: 845 704 2323 (SkypeIn)
> > > > ----------------------------------------------------
> >
> > ----------------------------------------------------
> > Marc Spiegelman
> > Lamont-Doherty Earth Observatory
> > Dept. of Applied Physics/Applied Math
> > Columbia University
> > http://www.ldeo.columbia.edu/~mspieg
> > tel: 845 704 2323 (SkypeIn)
> > ----------------------------------------------------

----------------------------------------------------
Marc Spiegelman
Lamont-Doherty Earth Observatory
Dept. of Applied Physics/Applied Math
Columbia University
http://www.ldeo.columbia.edu/~mspieg
tel: 845 704 2323 (SkypeIn)
----------------------------------------------------