How to compute 3D interpolation from data at points not on the mesh ?

Question

Suppose I have a set of points (x,y,z) and data at these points ( not a function written in math expression).

x y z F
-10 2 4 10.24
-10 2 6 5.98
and so on.

These points fill the whole domain (say a 3D box) but they are not the nodes of elements in the mesh. The question is can FEniCS find 3D function f(x,y,z) that interpolates the data? (I am going to use this function later for the PDE I want to solve). How do I do that?

Answer 1

Create (Delaunay) tetrahedronation of these points. Define CG1 function with your values on these points. Project to your new mesh. Note that projection on non-matching mesh (last step) does not work in parallel.

Comments

That's a concept you need to program. You may need to utilize external mesh generator for the first step.