Solution interpolation

[radlicka]

Can you please provide a simple example for interpolation of FEM solution (e.q. in the case of example 1) . All of the examples except example 13 end with the export of the solution to vtk file. But sometimes you need to work with the solution in Julia script. It would be very helpful, as getting through the code is a quite difficult task ...

Tomas

[fverdugo]

Hi @radlicka !

v = get_free_dof_values(uh) gives a plain Julia vector with the dof values of your solution uh. Is this what you need?

[radlicka]

No, this is not what I need. I need to know the value of the solution (or gradient) in a given point (x,y,z), which need not be a nodal point of the mesh. More specifically, I solve the axially symmetrical Laplace equation (2D problem: ∇(r ⋅∇ u ) = 0) and I need to know the potential on a line parallel to the axis of symmetry (r=0). Recently I have everything except the final solution interpolation.

[ericneiva]

Hi @radlicka,

You can take a look at this interpolation tutorial - soon available in Gridap tutorials -, which deals with how to interpolate FE functions in arbitrary points (Need at least Gridap v.0.16.4).

[fverdugo]

@radlicka you can evaluate the solution uh at a given arbitrary x::Point object, uh(x).

Important performance warning

If you want to evaluate uh at several points x1,... , xN , you have 2 options to perform this operation efficiently:

• [recommended] Store these points in a vector points= [ x1,... ,xN], and then evaluate uh(points)
• Build a cache object to reuse data between evaluations:

cache = return_cache(uh,x1)
evaluate!(cache,uh,x1)
evaluate!(cache,uh,x2)
...
evaluate!(cache,uh,xN)

[radlicka]

Perfect, thanks for a prompt answer. Tomas