Hi dealii users
I need to constrain all the support points on a Q2 element instead of only
vertices. The constrained values (inhomogeneity) are obtained from
(conceptually) a function, say f(\bold{x}). I already know how to query the
coordinates of the support points, I also know how to query their global
dof numbers, but I do not know *how the dof numbers are ordered*: for
example, what is the global dof number of the ith component of velocity at
support point v? Especially my finite element consists of a 2nd order
vector field (velocity) and a 1st order scalar field (pressure). Here is
the code snippet:
Quadrature<dim> q(fe.base_element(0).get_unit_support_points()); //
constraints will only be applied to the velocity dofs
MappingQGeneric<dim> mapping(1);
FEValues<dim> fe_values(mapping, fe.base_element(0), q,
update_quadrature_points);
std::vector<types::global_dof_index>
dof_indices(fe.base_element(0).dofs_per_cell);
for (auto cell = dof_handler.begin_active(); cell != dof_handler.end();
++cell)
{
fe_values.reinit(cell);
const vector<Point<dim>>& unit_points =
fe.base_element(0).get_unit_support_points();
*cell->get_dof_indices(dof_indices, 0);* // query the global dof numbers
on base element 0
for (unsigned int v = 0; v < unit_points.size(); ++v)
{
Point<dim> mapped_point = mapping.transform_unit_to_real_cell(cell,
unit_points[i]);
Vector<double> value = f(mapped_point); // Calculate the constrained
value based on the real coordinates of a support point
// set the inhomogeneity constraints on the velocity
for (unsigned int i = 0; i < dim; ++i)
{
// Now that I have dof_indices as a vector, but which component
correspond to the ith component of velocity at support point v?
*auto line = dof_indices[?]*
constraints.add_line(line);
constraints.set_inhomogeneity(line, value[i]);
}
}
}
Another related question is that, my computational results are written in
vtu format as Q1 elements, which makes the resolution very coarse. Is there
a way to write the results as 2nd order elements (ParaView supports it)? I
suppose the pressure component then needs to be interpolated as it is 1st
order?
Thank you very much!
Jie
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