Dear Simon,
Thank you for your reply. Your suggestion definitely works. I used
functions that output one component when I was interpolating scalar
potentials. It works well.
However, the FE_Nedelec is different. It implements edge elements. They are
vector-based. That is, functions are represented by a superposition of
vector-valued shape functions:
\vec{A} = \sum u_i vec{N}_i .
Therefore, the output of the "value" method in “class CustomFunction :
public Function” must be vector-valued. Three components in a
three-dimensional space. Otherwise, there is no point in interpolation.
This kind of vectorial approximations is a bread-and-butter topic in
magnetics. See, for example, equation (7) in:
https://ieeexplore.ieee.org/document/497322
In short, the source, i.e the current vector potential, must be projected
on the space spanned by the vector-valued shape functions. Otherwise, the
simulation is numerically unstable. The last, from my experience, is
definitely true.
Best,
John
On Fri, Apr 16, 2021 at 5:28 PM [email protected] <[email protected]>
wrote:
> Hi,
> I don't have any experience with FE_Nedelec, but the error message states
> that the function you are trying to interpolate has 1 component, while the
> element has dim components.
>
> If you implemented your own Function, you need to make sure it has
> dim-components by calling the constructor of Function with dim as
> inargument:
>
> template <int dim>
> class CustomFunction : public Function<dim>
> {
> public:
> CustomFunction()
> : Function<dim>(dim) // The function has dim components
> {}
>
> double
> value(const Point<dim> & point,
> const unsigned int component = 0) const override
> {
> // Return value will depend on component here
> return 0;
> }
> };
>
>
> Best,
> Simon
>
> On Friday, April 16, 2021 at 5:07:01 PM UTC+2 [email protected] wrote:
>
>> Hello,
>>
>> It seems I am unable to find a function similar to
>> VectorTools::interpolate for FE_Nedelec finite elements. The existing
>> implementation of this functions gives the following run-time error:
>>
>> *An error occurred in line <556> of file
>> </home/john/dealii-9.1.1/include/deal.II*
>>
>> */numerics/vector_tools.templates.h> in function*
>>
>> * void dealii::VectorTools::interpolate(const dealii::Mapping<dim,
>> spacedim>&,*
>>
>> * const DoFHandlerType<dim, spacedim>&, const dealii::Function<spacedim,
>> typename*
>>
>> * VectorType::value_type>&, VectorType&, const dealii::ComponentMask&)
>> [with int *
>>
>> *dim = 3; int spacedim = 3; VectorType = dealii::Vector<double>;
>> DoFHandlerType =*
>>
>> * dealii::DoFHandler; typename VectorType::value_type = double]*
>>
>> *The violated condition was: *
>>
>> * dof_handler.get_fe().n_components() == function.n_components*
>>
>> *Additional information: *
>>
>> * Dimension 3 not equal to 1.*
>>
>>
>> Looks like VectorTools::interpolate does not like the vector-valued
>> finite elements. Could you please point me in the right direction?
>>
>>
>> Best,
>>
>> John
>>
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