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[Florian Rathgeber <florian.rathgeber@xxxxxxxxxxxxxx>]

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I guess I haven't made my point very clear. The demo you gave is a good
example of what's currently possible and where the limit is I think.

Say you take dolfin/demo/pde/spatial-coordinates/cpp and want to
restrict the source term f to only a circle in the center of the domain.
How would you do that? I wouldn't know another way than a conditional
and I couldn't find a way to get that working with FFC.

I was not talking about constants, but about expressions that are not
uniform over the whole domain, should have made that more clear.

Florian

On 23.07.2010 13:51, Kristian Ølgaard wrote:
> On 23 July 2010 12:40, Florian Rathgeber
> <florian.rathgeber@xxxxxxxxxxxxxx> wrote:
> Hi,
> 
> Profiling DOLFIN assembly shows that for forms with many coefficients or
> computationally expensive expressions assigned to coefficients, a great
> deal of the whole assembly is spent in expression evaluation.
> 
> An idea I wanted to investigate was giving an expresssion in UFL and
> have FFC generate corresponding code to evaluate it inline during tensor
> tabulation. That should have the potential of eliminating some of the
> overhead.
> 
> However, currently that is only possible within very limited bounds. FFC
> does not yet support UFL conditionals, which essentially limits possible
> expressions to depend on coordinates only and be the same over the whole
> domain (which is not very useful for most form coefficients, e.g. source
> terms).
> 
>> Did you have a look at the dolfin/demo/pde/spatial-coordinates/cpp
>> demo? It is essentially the dolfin/demo/pde/poisson/cpp demo but it
>> uses source and boundary terms defined using coordinates and is not
>> the same over the whole domain (I don't really get your point here).
>> The coordinates are defined as the coordinates of the current
>> integration point located on the current cell which is being
>> integrated. Have a look at the generated code, then it might be
>> clearer what's going on.
> 
>> Kristian
> 
> This brings me to my questions:
> 1) Do you see a reasonable chance for speeding up assembly in the way
> described?
> 2) Is my assessement correct? Or do I miss some capabilities of FFC that
> support my use case?
> 3) Since UFL basically support arbitrary python syntax, would it be
> reasonable to support translation for user-defined Expressions given in
> python (either overloading eval in a class defived from Expression or
> passing C++ code to the SWIG constructor of Expression)? FFC would
> generate code to evaluate these Expressions inline during tensor
> tabulation. That would of course require the Expression to be stateless
> and have not input other than the coordinates. But at least it would
> provide much more flexibility and also consistency with the DOLFIN
> interface in general
> (sidenote: it is possible to specify Expressions in this way in UFL, but
> they are treated just like Coefficients by FFC)
> 
> Illustration example (UFL file):
>  from dolfin import Expression
> 
>  code_expr = """
>  class Source : public Expression
>  {
>  public:
>    void eval(Array<double>& values, const Array<double>& x) const
>    {
>      values[0] = ((x[0]-0.25)*(x[0]-0.25)+(x[1]-0.5)*(x[1]-0.5) <
> 0.025) ? 1.0 : 0.0;
>    }
>  };
>  """
> 
>  scalar = FiniteElement("Lagrange", triangle, 1)
> 
>  v  = TestFunction(scalar)
>  u  = TrialFunction(scalar)
>  u0 = Coefficient(scalar)
>  f = Expressions(code_expr)
> 
>  c = 0.05
>  k = 0.1
>  alpha = 1.0
> 
>  a = v*u*dx + k*alpha*u*v*dx + k*c*dot(grad(v), grad(u))*dx
>  L = v*u0*dx + k*v*f*dx
> 
> Florian
>>
>>
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