dolfin team mailing list archive

[Anders Logg <logg@xxxxxxxxx>]

On Wed, Oct 22, 2008 at 10:00:07PM +0200, Martin Sandve Alnæs wrote:
> 2008/10/22 Anders Logg <logg@xxxxxxxxx>:
> > On Wed, Oct 22, 2008 at 07:45:03PM +0100, Garth N. Wells wrote:
> >>
> >>
> >> Anders Logg wrote:
> >> > On Wed, Oct 22, 2008 at 08:24:18PM +0200, Anders Logg wrote:
> >> >> On Wed, Oct 22, 2008 at 07:05:09PM +0100, Garth N. Wells wrote:
> >> >>>
> >> >>> Anders Logg wrote:
> >> >>>> On Wed, Oct 22, 2008 at 12:08:43PM +0100, Garth N. Wells wrote:
> >> >>>>> The thread on the new Function design has digressed from the immediate
> >> >>>>> issue, so I'm restarting it.
> >> >>>>>
> >> >>>>> The issue is how to deal with user defined functions in C++. What if we
> >> >>>>> have a design such that:
> >> >>>>>
> >> >>>>> - All Functions must have a FunctionSpace
> >> >>>> Yes.
> >> >>>>
> >> >>>>> - A FunctionSpace does not have to be complete (a complete FunctionSpace
> >> >>>>> having a Mesh, a FiniteElement and a DofMap). As a minimum requirement,
> >> >>>>> and FunctionSpace must have a Mesh.
> >> >>>> I think it should always need to be complete. We can avoid a lot of
> >> >>>> trouble if we make firm requirements: a Function is always associated
> >> >>>> with a FunctionSpace and the FunctionSpace is always completely
> >> >>>> defined.
> >> >>>>
> >> >>>>> - A FiniteElement and/or DofMap can be attached to a FunctionSpace after
> >> >>>>> its creation
> >> >>>>>
> >> >>>>>
> >> >>>>> Related to the functions Function::interpolate(double* coefficients, ..)
> >> >>>>> for interpolating Functions on cells
> >> >>>>>
> >> >>>>> - The new Function::interpolate functions do not take a FiniteElement as
> >> >>>>> an argument, so it is not possible to interpolate a function in a
> >> >>>>> different space. Is it desirable to allow Functions from one space to be
> >> >>>>> interpolated in another?
> >> >>>> Yes, it's desirable. This can be done globally when needed:
> >> >>>>
> >> >>>>   Function v(V);
> >> >>>>   Vector coefficients;
> >> >>>>   v.interpolate(coefficients, W);
> >> >>>>
> >> >>>> This will compute the global coefficient vector for v on W.
> >> >>>>
> >> >>>> This is currently implemented with the assumption that the meshes for
> >> >>>> V and W are the same but could quite easily be extended to
> >> >>>> non-matching meshes now that functions can be evaluated at arbitrary
> >> >>>> points (using GTS).
> >> >>>>
> >> >>>>> If we do this, would:
> >> >>>>>
> >> >>>>> - The above allow FiniteElement types to be checked at runtime for
> >> >>>>> consistency (the FiniteElement passed to Function::interpolate should be
> >> >>>>> the same as the Functions own FiniteElement for discrete Functions. This
> >> >>>>> is what we did with the old design.)>
> >> >>>>>
> >> >>>>> - The above deal with the issue of user-defined functions which have a a
> >> >>>>> FunctionSpace but no FiniteElement?
> >> >>>>>
> >> >>>>> - The above deal with special functions, like the mesh size h?
> >> >>>> Here's my suggestion for how to handle initialization of Functions in C++.
> >> >>>> There is no need for a circular dependency. First some simple facts:
> >> >>>>
> >> >>>>   1. The constructor of a Form may require one or more Functions
> >> >>>>   2. The constructor of a Function requires a FunctionSpace
> >> >>>>
> >> >>>> From this it follows that we must do something like
> >> >>>>
> >> >>>>   Function f(V);
> >> >>>>   Poisson::BilinearForm a;
> >> >>>>   Poisson::LinearForm L(f);
> >> >>>>
> >> >>>> The question is now how to initialize the FunctionSpace V. My
> >> >>>> suggestion would be to extend the code generation to generate code for
> >> >>>> creating the FunctionSpace(s), just like we do already when we
> >> >>>> generate UFC code + some extra code for defining the Form classes
> >> >>>> (when using -l dolfin in FFC). This does not make FFC DOLFIN-specific
> >> >>>> or DOLFIN FFC-specific. One can still use other form compilers, but the
> >> >>>> interface will not be as nice.
> >> >>>>
> >> >>>> So, one would do something like this:
> >> >>>>
> >> >>>>   #include "Poisson.h"
> >> >>>>
> >> >>>>   int main()
> >> >>>>   {
> >> >>>>     Mesh mesh("mesh.xml");
> >> >>>>     Poisson::TestSpace V(mesh);
> >> >>> Why 'TestSpace'?
> >> >>>
> >> >>> Also, when many functions are present, how would we
> >> >>> identify each one? Could FFC create a class Poisson::FunctionSpace::foo
> >> >>> when 'foo' is the name of the function in the FFC input?
> >> >> We could let FFC create a number of function space classes:
> >> >>
> >> >>   Poisson::TestSpace
> >> >>   Poisson::TrialSpace
> >> >>   Poisson::FunctionSpace_0
> >> >>   Poisson::FunctionSpace_1
> >> >>   ...
> >> >>
> >> >> or even
> >> >>
> >> >>   Poisson::v::FunctionSpace
> >> >>   Poisson::u::FunctionSpace
> >> >>   Poisson::f::FunctionSpace
> >> >>   Poisson::g::FunctionSpace
> >> >>
> >> >> (but I'm not sure it looks very nice).
> >> >>
> >> >> A complication I didn't think of before is how to handle the case when
> >> >> all spaces are the same (to get reuse of dofmaps). One option would be
> >> >> to either generate just one class if all spaces are the same, and
> >> >> otherwise generate separate clases like above. So either one does
> >> >>
> >> >>   Poisson::FunctionSpace V(mesh);
> >> >>   Function f(V);
> >> >>   Function g(V);
> >> >>   Poisson::LinearForm(f, g);
> >> >>
> >> >> or
> >> >>
> >> >>   Poisson::FunctionSpace_0 V(mesh);
> >> >>   Poisson::FunctionSpace_1 W(mesh);
> >> >>   Function f(V);
> >> >>   Function g(W);
> >> >>   Poisson::LinearForm(f, g);
> >> >>
> >> >>>>     Function f(V);
> >> >>>>     Poisson::BilinearForm a;
> >> >>>>     Poisson::LinearForm L(f);
> >> >>>>     ...
> >> >>>>   }
> >> >>>>
> >> >>>> First V, then f, then L.
> >> >>>>
> >> >>> Would this work for all the Functions in SpecialFunction.h?
> >> >> I haven't thought about it, but yes I guess it would.
> >> >>
> >> >> We can provide a set of predefined FunctionSpaces (like DG on
> >> >> triangles and tetrahedra).
> >> >
> >> > I'm moving the discussion of the removal of DofMapSet over here since
> >> > it's related.
> >> >
> >> > If a Form should own a set of FunctionSpaces (replacing the current
> >> > DofMapSet), that would prevent reuse of FunctionSpaces (and DofMaps)
> >> > across multiple Forms.
> >> >
> >> > Another option would be to always require that a Form is initialized
> >> > with one or more FunctionSpaces. This makes sense and is in agreement
> >> > with the requirement of a FunctionSpace when initializing a Function.
> >> >
> >> > It would then be
> >> >
> >> >   PoissonFunctionSpace V(mesh);
> >> >   Function f(V);
> >> >   Function g(V);
> >> >   PoissonBilinearForm a(V, V);
> >> >   PoissonLinearForm L(V, f, g);
> >> >
> >> > Then it's possible to reuse V across multiple forms (even forms not
> >> > included in Poisson.h).
> >> >
> >>
> >> Could work. To keep things clear cut, I would use
> >>
> >>     PoissonFunctionSpace V(mesh);
> >>     Array<FunctionSpace*> VxV(V, V);
> >>     PoissonBilinearForm a(VxV);  // Might also nee a shared_ptr version
> >>     PoissonLinearForm L(V, f, g);
> >>
> >> The first argument to a Form defines the test and/or trial spaces, the
> >> other arguments are the Functions in the Form.
> >>
> >> Garth
> >
> > That looks like a complication. The constructor of a Form takes a
> > variable number of arguments anyway, so it's no big deal to require
> > one FunctionSpace for a linear form and two for a bilinear form.
> > It also looks nicer (avoiding Array and pointers).
> >
> 
> The good thing about it is that it allows building the argument list
> dynamically depending on input parameters.

When is that necessary?

If it's needed it's simple enough to generate code for both: one
constructor that takes (V, V) and one that takes VxV.

> A potential issue with generating FunctionSpace subclasses
> is sharing a FunctionSpace between forms compiled separately.
> That is easily handled though: FooForm need to take FunctionSpace
> as input and check for compatibility with FooFunctionSpace.

Yes, checks are needed.

-- 
Anders

Attachment: signature.asc
Description: Digital signature