FE_Q<dim>(p) with p>1: Global coordinates of midnodes

[Simon]

Dear All,

I am implementing a local postprocessing SPR-Approach for a mechanical problem, in which I sloppy speaking need the global coordinates of all nodes.

I use Elements of type FE_Q<dim>(p).

For p=1 there is no problem: I can simply loop over all cells and vertices and use cell->vertex(...) in order to get the global coordinates of vertex(...).

Being p=2 for instance, this approach does not work anymore. In this case is there an easy way to figure out the coordinates of midnodes as well?

Thanks for help!

Best

Simon

[Paras Kumar]

Hi Simon,

This could be helpful: https://github.com/dealii/dealii/wiki/Frequently-Asked-Questions#how-to-get-the-mapped-position-of-support-points-of-my-element

Here's a code snippet for Option-1, which I usually use.

const auto &               feSystem       = dofHandler.get_fe();
dealii::MappingQ<dim, dim> cellMapping(feSystem.degree);
const auto &               referenceCellSupportPoints =  feSystem.get_unit_support_points();
std::vector<dealii::Point<dim>> realCellSupportPoints(referenceCellSupportPoints.size());
unsigned int supportPointCtr = 0;
for (const auto &supportPoint : referenceCellSupportPoints)
  {
    realCellSupportPoints[supportPointCtr] =
      cellMapping.transform_unit_to_real_cell(cellIter, supportPoint);
    ++supportPointCtr;
  }

Best regards,

Paras

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[Simon]

Hi Paras,

everything worked fine, thanks a lot!

Best

Simon

[Wolfgang Bangerth]

On 4/19/21 4:14 AM, Simon wrote:
>
> I use Elements of type FE_Q<dim>(p).
> For p=1 there is no problem: I can simply loop over all cells and vertices and
> use cell->vertex(...) in order to get the global coordinates of vertex(...).
> Being p=2 for instance, this approach does not work anymore. In this case is
> there an easy way to figure out the coordinates of midnodes as well?

In addition to Paras' approach, you can also take a look at
DoFTools::map_dofs_to_support_points().

Best
W.

--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/