dolfin team mailing list archive

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

Shawn Walker wrote:
> The thing that has been confusing me about this, is the need for a form. 
> By form you mean a weak/variational form of a PDE, right?  

Yes.

But what does
> this have to do with defining a discrete function?  A discrete function 
> only depends on a set of basis functions.  Of course, you need a DoFmap, 
> but that still doesn't require a bilinear form.  

Correct, a form doesn't have anything to with defining a function from a 
particular space, but a form requires functions that do come from a 
known function space. We can't just pass around a pointer to a function 
that returns exp(x^2 + y^2), we need to attach a basis to the function. 
This last point is what we're grappling with in the case of user-defined 
functions.

Garth

Even a (finite element)
> function space does not depend on a particular form (e.g. H^1 could be 
> used for many different variational problems).
>
> I'm probably missing something.  I still don't know the whole dolfin/ffc 
> setup yet.  I appreciate any help you can give.
>
> - Shawn
>
> On Tue, 21 Oct 2008, Garth N. Wells wrote:
>
> > Shawn Walker wrote:
> > > I may be missing part of the argument here, but for the case when a 
> > > user defined function is something like exp(x^2 + y^2), could we just 
> > > pass a function pointer (for this particular function) to the 
> > > interpolation routine?  In MATLAB, this type of thing is easy because 
> > > of function handles.  I know we don't have that luxury, but a 
> > > function pointer kind of does this.
> > >
> > > Sorry, if I am not understanding the issue.
> >
> > The difficulty is that all the functions in a form come from a finite 
> > element space, and the space determines where we need to evaluate the 
> > functions. Before, DOLFIN figured out the appropriate space, and 
> > user-defined function were interpolated in this space,
> > but it made the design complex when handling different function types. 
> > What we aim for now is to have all Functions fully-defined (but we'd 
> > like to keep it simple for users too).
> >
> > Garth
> >
> > > - Shawn
> > >
> > > On Tue, 21 Oct 2008, Garth N. Wells wrote:
> > >
> > > > Anders Logg wrote:
> > > > > On Tue, Oct 21, 2008 at 04:45:01PM +0100, Garth N. Wells wrote:
> > > > > > I have a few questions and thoughts regarding the new Function design
> > > > > >
> > > > > > * It's not clear to me what the intention is with user-defined
> > > > > > functions. The functions Function::interpolate(...) never call 
> > > > > > eval(..),
> > > > > > so they can't pick up user-defined values. Should 
> > > > > > Function::interpolate
> > > > > > test for the presence of a GenericVector to decide whether or not the
> > > > > > Function is discrete or user-defined?
> > > > >
> > > > > Yes, sorry. I've missed this. I'll fix it.
> > > > >
> > > > > > * It would be useful to declare user-defined functions without
> > > > > > associating a FunctionSpace. If we want to interpolate the 
> > > > > > function, a
> > > > > > FunctionSpace must then be provided. Anyone see any problems with 
> > > > > > this?
> > > > >
> > > > > The reasoning here is that all Functions must always be associated
> > > > > with a FunctionSpace so that they may be correctly interpreted in
> > > > > forms and correctly plotted. When a Function is created in PyDOLFIN,
> > > > > it must always be associated with a certain FiniteElement (and in a
> > > > > while FunctionSpace). It would simplify the handling of Functions if
> > > > > they are always associated with a FunctionSpace.
> > > >
> > > > I agree that is makes life simple if every function has a space, but it
> > > > is a bit clunky for declaring user-defined functions. The forms must be
> > > > declared first to extract the finite element to create the function
> > > > space. Could look nasty when a lot of functions are involved.
> > > >
> > > > We have a function Function::interpolate which takes a function space V
> > > > as an argument and it interpolates the function u in V. What if we
> > > > permit undefined function spaces (which perhaps only have a domain)? We
> > > > would then interpolate the user defined function u in the provided 
> > > > space V.
> > > >
> > > > Garth
> > > >
> > > > > ------------------------------------------------------------------------ 
> > > > >
> > > > >
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