That means that I don't have to create that matrix myself, but rather use
the matrix I get from FE_Q_*::get_interpolation_matrix()?
The most interesting bug my code has at the moment is:
Q(a)->B(b): I get identical vectors, i.e. a == b
B(b)->Q(a): Vectors are not identical anymore, a != b
Q(a)->B(b): Even though that worked in the first round, it does not in the
second, a != b
I do not understand that behavior yet.
Am Donnerstag, 30. Mai 2019 19:00:02 UTC+2 schrieb Wolfgang Bangerth:
>
> On 5/30/19 9:06 AM, 'Maxi Miller' via deal.II User Group wrote:
> > I wanted to write some functions to convert my solution from using
> > FE_Q-elements to FE_Bernstein-elements (and back). For that I wrote two
> > functions, convert_feQ_to_feB() and convert_feB_to_feQ() (as listed in
> the
> > attachment). When converting from FE_Q-elements to
> FE_Bernstein-elements, I
> > get the same values for input and output, but on the way back I get
> wrong
> > values (currently I am just using a vector filled with the value 1), but
> I can
> > not find the reason why the conversion back is failing. Did I forget
> something
> > in the corresponding function?
>
> I have to admit that I don't have the time right now to look at your code,
> but
> it's really just an interpolation problem to go from FE_B to FE_Q: you
> need to
> evaluate each shape function of the FE_B at the interpolation (=support)
> points of the FE_Q. This gives you a cell-local matrix of the form
> B_{ij} = \varphi_{Bernstein,j)(x_{j,Q})
> (or with indices reversed -- check with the documentation).
>
> By the way, the place to implement this is in the
> FE_Q_Base::get_interpolation_matrix() function for B -> Q (see
> source/fe/fe_base.cc around line 500), and maybe
> FE_Q_Bernstein::get_interpolation_matrix() if you come up with a clever
> way to
> define the operation. I know that the latter function says that you can't
> do
> it, but I suspect that if you at least define it in a way so that the
> interpolation of a function onto itself is the identity operation, and if
> the
> interpolation of a FE_Q function onto FE_Bernstein yields the same,
> continuous
> function, then it might still go into that place.
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: bang...@colostate.edu
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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