Efficiently Finding Maximum Function Value in a Mesh with FEniCSx

[dokken]

@nikoleeaa

Okay. What I mean is, if the function space is not “Lagrange 1” and the degrees of freedom are not located at the vertices of each cell, is there aother method to obtain the coordinates of the cell vertices?

There is a vertex to dof map:

Application of point forces, mapping vertex indices to corresponding DOFs

Here is a vectorized version of the code above (credit to @dokken) def vertex_to_dof_map_original(mesh, V): num_vertices = ( mesh.topology.index_map(0).size_local + mesh.topology.index_map(0).num_ghosts ) vertex_to_dof_map = np.empty(num_vertices, dtype=np.int32) num_cells = ( mesh.topology.index_map(mesh.topology.dim).size_local + mesh.topology.index_map(mesh.topology.dim).num_ghosts ) c_to_v = mesh.topology.connectivity(mesh.topology.dim, 0) …

which you can use to map vertices to dogs.

Combine that with entities_to_geoemtry, and you can get the values at vertices for any space that has dofs associated with vertices.

Note that for higher order spaces you are then excluding all other dofs, and you will likely not get the correct maximum value.