On 23 July 2010 13:02, Florian Rathgeber
<florian.rathge...@googlemail.com> wrote:
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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.
Now it makes more sense, I think you would need a conditional indeed.
> 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.rathge...@googlemail.com> 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
I think it sounds complicated, much better to defined the function
directly in terms of coordinates.
>> (sidenote: it is possible to specify Expressions in this way in UFL, but
>> they are treated just like Coefficients by FFC)
I don't think this is the case, it is possible in the Python interface
to DOLFIN, but not in UFL.
>> 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;
>> }
>> };
>> """
In UFL you can do:
f = conditional( (x[0]-0.25)**2 + (x[1]-0.5)**2 < 0.025), 1.0, 0.0 )
although no output is generated yet because Conditionals are not
supported yet, but the code which will be generated should look an
awful lot like what you have i.e.
f = ((x[0]-0.25)*(x[0]-0.25)+(x[1]-0.5)*(x[1]-0.5) < 0.025) ? 1.0 : 0.0;
Kristian
>> 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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>>>
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