Using basix, I’m getting reference points mapped to wrong physical points. See below
import basix
import basix.ufl
import numpy as np
def compute_physical_points(nodes_coords, x_ref):
"""
Parameters
----------
nodes_coords : np.array(shape=(n, 2))
node coords of the mesh cell
x_ref : np.array(shape=(m, 2))
points in the reference cell
Returns:
-------
np.array(shape=(m, 2))
Physical points in the cell.
"""
element = basix.ufl.element("Lagrange", "quadrilateral", 1)
basis_values = element.tabulate(0, x_ref)
x = basis_values[0, :, :] @ nodes_coords
return x
nodes_coords = np.array([[0, 0], [1, 0], [1, 1], [0, 1]])
x_ref = np.array([[0.5, 0.5], [0.5, 0.25], [0.25, 0.5], [0.25, 0.25]])
print(compute_physical_points(nodes_coords, x_ref))
The output is
[[0.5 0.5 ]
[0.5 0.25 ]
[0.5 0.5 ]
[0.375 0.25 ]]
The second and third point (row) are x_ref is wrongly mapped. In fact, the first and third point are mapped to the same physical point.