On Tue, Jan 29, 2008 at 08:33:01AM -0500, Jake Ostien wrote:
Dag Lindbo wrote:
Hello all,
I saw that there is a convenient way to evaluate a DiscreteFunction at
all vertices of its mesh, i.e. u.evaluate( val ). Is there a convenient
way to evaluate a function on each cell (e.g. on the mid-point of each
triangle)?
If not, I would really appreciate some suggestions how to go about. Is
the more general function
interpolate(real* coefficients,const ufc::cell& cell,
const ufc::finite_element& finite_element)
the way to go? How do I evaluate the sum of basis functions in a point
if I know the coefficients?
I have been playing with a similar functionality in my own project,
where I need to evaluate some field on a cell. What I ended up doing is
adding two methods to the Function class, specifically for
DiscreteFunctions, that return the local data, uint* dofs (which are the
coefficients) and the DofMap* dof_map. Then I can iterate over cells
and evaluate the coefficients on each cell however I want. So my loop
looks something like:
(say field is a DiscreteFunction)
for (; !cell.end(); ++cell) {
ufc_cell.update(*cell);
dof_map->tabulate_dofs(dofs, ufc_cell);
field.vector().get(array, dof_map->local_dimension(), dofs);
...do something with array...
}
There is probably a better way to do this, and I'd like to hear it,
too. Otherwise I can submit my own changes.
Jake
What type of function is it that you want to evaluate on cells?
Is it a finite element function? Defined by what element? Or is it a
user-defined function, something like sin(x)?
In any case, the best way to compute the values on cells would be to
just define a projection to piecewise constants. Then all values will
be in the Vector() that holds the degrees of freedom (if you should
need them).
Here's an example:
element = FiniteElement(your space here)
DG0 = FiniteElement("DG", "your shape", 0)
v = TestFunction(DG0)
u = TrialFunction(DG0)
f = Function(element)
a = v*u*dx
L = v*f*dx
Solve the system and u will be the projection of f onto constants.
