Dear all,
I am currently implementing an Eigenstrain solver. For this purpose I have
currently defined an FESystem via
FESystem<3> fe(FE_Q<3>(1), 3);
with the FEValuesExtractors
constFEValuesExtractors::Vector displacements(0);
The DoFs are subsequently distributed using the regular
DoFHandler<3> dof_handler(triangulation);
dof_handler.distribute_dofs(fe);
At the moment I have a function which computes the eigenstrain at a given
point
class EigenstrainFunction : public TensorFunction<2, 3>
{
public:
virtual Tensor<2, 3> value(const Point<3> &p) const {
Tensor<2, 3> eigenstrain;
// some rather expensive computation
return plastic_eigenstrain;
}
};
and during the assembly of my right hand side this function gets called at
the quadrature points.
So far so good.
But now I would like to have the eigenstrain in my VTK output as well,
exactly as the program "sees" it, i.e. in a way that the values at the
quadrature points are preserved.
To my understanding the correct way to do this is to use one of the
VectorTools::project routines to get respective values at the degrees of
freedom.
Unfortunately the eigenstrain does not have any corresponding degrees of
freedom.
And projecting the values would again lead to an evaluation of this rather
expensive function at the exact same quadrature points that I have already
done an evaluation on.
What is the most elegant solution to this problem under the constraint,
that the function should only be called once per quadrature point?
Options that come to mind, which I am absolutely not sure about whether
they are even feasible:
- As my eigenstrain matrix is symmetric I could pack it into two
solution vectors and reuse the DoFHandler from the 3 component displacement
to get the projected components, then use them in the assembly of the right
hand side to interpolate their values at the quadrature points using the
shape functions.
- I could set up another FESystem
FESystem<3> elasticity_element(FE_Q<3>(1), 3);
FESystem<3> eigenstrain_element(FE_Q<3>(1), 6);
FESystem<3> fe(elasticity_element, 1, eigenstrain_element, 1);
but could I then use FEValuesExtractors::SymmetricTensor on the
eigenstrain element? And could I only project my function onto the
eigenstrain element?
Best regards,
Dominik
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