[dune-fem] Interpolating a function of a 3D grid over a 2D grid

[Andreas Dedner]

Hi.
Perhaps having a look at the grid-glue module could help?
Best
Andreas

On 20/11/13 14:51, Tobias Malkmus wrote:
> Hi Andrea
>
> They key ingrediens for a fast interpolation is to compute the
> intersection between the 3D and the 2D grid.
>
> >     { phi3D_.evaluate (x, y); }
>
> searches in the 3D grid the element in which x is located.
> So for each evaluation of your interface function at most a grid
> traversal over the 3D grid is needed.
>
> If you can find a way to couple a 3D and 2D grid you can speed up this
> interpolation. Since i deal with similar problems i would write
> something like an IntersctionGridPart which chaches the pairs of
> entities of the 2D and 3D grid which have a non empty intersection.
>
> As far as i know there is no official implementation to this.
>
> Best Tobias
>
>
> On 11/20/2013 03:42 PM, Sacconi, Andrea wrote:
>> Hi everyone,
>>
>> I would like to ask you a question about interpolation.
>> I am dealing with a coupled domain-interface problem, where a
>> function (the electric potential) defined over the 3D domain grid has
>> to be evaluated on a 2D grid which represents the interface.
>> Now, I cannot use the usual interpolation because the two functions
>> are defined over different grids (with different dimensions, too), so
>> I am currently following this way: I create a function that has only
>> the global evaluate method:
>>
>> template < class DiscreteFunction3DType , class
>> ScalarCurvatureFunctionSpaceType >
>> class Phi3D : public Dune::Fem::Function <
>> ScalarCurvatureFunctionSpaceType, Phi3D < DiscreteFunction3DType ,
>> ScalarCurvatureFunctionSpaceType > >
>> {
>> public:
>>
>>     typedef typename DiscreteFunction3DType :: DomainType DomainType;
>>     typedef typename DiscreteFunction3DType :: RangeType RangeType;
>>
>>     Phi3D ( const DiscreteFunction3DType & phi3D_original ) : phi3D_
>> ( phi3D_original ) {}
>>     
>>     void evaluate (const DomainType & x, RangeType & y) const
>>     { phi3D_.evaluate (x, y); }
>>
>> private:
>>     DiscreteFunction3DType phi3D_;
>> };
>>
>> then I can interpolate an instance of the Phi3D class using the
>> Lagrange interpolation over the 2D grid.
>> Is there a faster/cleverer way of doing it? With tetrahedra and
>> triangles it really takes ages, especially when the grid is refined.
>>
>> Cheers,
>> Andrea
>> __________________________________________________________
>>
>> Andrea Sacconi
>> PhD student, Applied Mathematics
>> AMMP Section, Department of Mathematics, Imperial College London,
>> London SW7 2AZ, UK
>> a.sacconi11 at imperial.ac.uk
>>
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>>
>>
>
>