Hermite coordinate element

script.py

"""
Hermite as coordinate element in DOLFINx
Author: Jørgen S. Dokken
SPDX License identifier: MIT
"""

from mpi4py import MPI
import dolfinx

import basix.ufl
import numpy as np
import ufl

element = basix.ufl.element(
    basix.ElementFamily.serendipity,
    basix.CellType.hexahedron,
    2,
    lagrange_variant=basix.LagrangeVariant.equispaced,
    dpc_variant=basix.DPCVariant.simplex_equispaced,
    shape=(3,),
)


elements = np.array(
    [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19]],
    dtype=np.int64,
)
nodes = np.array(
    [
        [0, 0, 0],
        [1, 0, 0],
        [0, 1, 0],
        [1, 1, 0],
        [0, 0, 1],
        [1, 0, 1],
        [0, 1, 1],
        [1, 1, 1],
        [0.5, 0, -0.1],
        [0, 0.5, 0],
        [0, 0, 0.5],
        [1, 0.5, 0],
        [1, 0, 0.5],
        [0.5, 1, 0],
        [0, 1, 0.5],
        [1, 1, 0.5],
        [0.5, 0, 1],
        [0, 0.5, 1],
        [1, 0.5, 1],
        [0.5, 1, 1],
    ],
    dtype=np.float64,
)

c_el = ufl.Mesh((element))

mesh = dolfinx.mesh.create_mesh(MPI.COMM_WORLD, elements, nodes, c_el)

V = dolfinx.fem.functionspace(mesh, element)
u = dolfinx.fem.Function(V)
u.interpolate(lambda x: (x[0], x[1], x[2]))

V_out = dolfinx.fem.functionspace(mesh, ("Lagrange", 2, (3,)))
u_out = dolfinx.fem.Function(V_out)
u_out.interpolate(u)
with dolfinx.io.VTXWriter(mesh.comm, "output.bp", [u_out]) as writer:
    writer.write(0.0)