Hi, I will write a small test case tomorrow for the
project_boundary_values() function tomorrow.
For the compute_nonzero_normal_flux(), I want to generate a a constraint
like this:
Require that $q\in W_h$ is such that for all test functions $\lambda \in
\Trace V_h$ we have
$$
0 = \int_{\Gamma_N} \lambda ((q-g)\dot \eta) \dee x
$$
Here, $W_h$ is fe_dgq^dim and $V_h$ is fe_dgq, both of the same degree (or
fe_dgp in both places).
I do this now by building a matrix for each cell $\Omega_i$ like
$$
\int_{\Gamma_N\cap \partial \Omega_i} \lambda (q\dot \eta)\dee x
$$
for test functions in $V_h$ (not just $Trace V_h$), then I use the singular
value decomposition of this matrix to remove (really just identify)
linearly dependent rows of this matrix, and store the results in normal
SparseMatrices. This technique works but is hard for me to understand.
The complexity of the code and your comments from before make me want to
handle the boundary conditions in a more idiomatic fashion.
Thanks for responding, I appreciate it
On Thursday, June 22, 2017 at 9:45:06 PM UTC-4, Wolfgang Bangerth wrote:
>
>
> > I am interersted in extending the functions
> > vector_tools::project_boundary_values() and
> > vector_tools::compute_nonzero_normal_flux() or writing something similar
> to
> > extend functionality to fe_dgq and fe_dgp finite elements. I am writing
> here
> > to ask for advice about this.
> >
> > My understanding is that this currently is not possible because those
> fe's
> > don't have unit support points. Is this correct? I have hacked
> together a
> > solution to get around this, but I want to clean up my code and do it
> > idiomatically now.
>
> I see no reason why project_boundary_values() shouldn't already work. It
> shouldn't need nodal elements. Writing a small test for it is probably the
> way
> to go to figure out whether it already works -- making the test into one
> for
> the testsuite would of course be even better!
>
> As for compute_nonzero_normal_flux() -- that is more complicated. How do
> you
> intend to make that work for non-nodal elements?
>
> Best
> W.
>
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth email: [email protected]
> <javascript:>
> www: http://www.math.colostate.edu/~bangerth/
>
>
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