Dear Praveen,
Regarding the performance of your code, there are several fundamental
problems:
- You run the constructor of Quadrature (allocates memory) and FEValues
(allocates lots of memory, evaluates a number of things you don't need)
that are both not made for use within the scenario of FEFieldFunction or
your manual loop.
- Since you're only using the shape values, you could skip all the
FEValues stuff and simply run the loop as
solution += solution0(local_dof_indices[i]) * fe.shape_value(i, p_ref);
- At this point, the performance depends on the
transform_real_to_unit_cell (which might be slow due to Newton
iterations) and the polynomial evaluation of fe.shape_value and to some
extent the virtual function call of the latter. It depends on your
polynomial space whether this is expensive.
- You could speed up the polynomial evaluation significantly if the
polynomial basis had a way to evaluate all polynomials at once - one
could use the tensor product structure here. If you're interested, I
could give you some code to do that.
I am not aware of any generic performance optimization beyond that level
for generic mappings, but I'm also not an expert of semi-Lagrangian
methods. The works that I know of do usually work on Cartesian grids
where one can get tremendous speedups of the
transform_real_to_unit_cell. Then you spend most of the time in the
polynomial interpolation steps again - but probably a factor of 100
faster than with what you have now.
Best,
Martin
On 05.09.2017 15:18, Praveen C wrote:
> Hello Bruno
>
>> Are you sure that FEFieldFunction.value() is the slowest part? In
>> 3D, point_inside could also be slow (you may need to do a few Newton
>> Iterations). It would be nice if you ran your code using a profiler
>> to see what is the bottleneck (building the quadrature in value(p1),
>> the evaluation itself, etc.).
>>
>
> If I comment out call to FEFieldFunction.value(), the code runs a LOT
> faster, so there is no doubt this is the slow part. I am in 2-d at
> present.
>
> I have set the correct cell by call to set_active_cell. Does the value
> function again check if the point is in this cell ?
>
> I implemented my own function to evaluate the solution as follows, but
> this is equally slow. I havent used a profiler but will timing parts
> of this below function be useful ?
>
> template<intdim>
> doubleProblem<dim>::evaluate_solution
> (typenameDoFHandler<dim>::active_cell_iterator cell,
> constPoint<dim> &p) const
> {
> // Transform p to unit cell
> Point<dim> p_ref = mapping.transform_real_to_unit_cell(cell, p);
>
> // Create quadrature rule
> Quadrature<dim> quadrature(p_ref);
>
> FEValues<dim> fe_values (mapping,
> fe,
> quadrature,
> update_values);
> std::vector<types::global_dof_index> local_dof_indices
> (fe.dofs_per_cell);
>
> fe_values.reinit(cell);
> cell->get_dof_indices (local_dof_indices);
> doublesolution = 0.0;
> for(unsignedinti=0; i<fe.dofs_per_cell; ++i)
> solution += solution0(local_dof_indices[i]) *
> fe_values.shape_value(i, 0);
>
> returnsolution;
> }
>
> I am processing one point at a time which could be slow. I am now
> rewriting the code so that all points falling in a cell are evaluated
> at once.
>
> Thanks
> praveen
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