Assembling Global Node Vector from Distributed Mesh in Parallel Computation

mesh
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Please note that if h comes from a function, it needs to be mapped to the mesh nodes.
See for instance: Moving submesh diverges from its designated trajectory in a two-phase problem - #2 by dokken

It is quite easy to gather the local mesh geometry and topology, as each of them has an index map that can be used to map from local to global indices.

An illustration of this is done with:

from mpi4py import MPI

import dolfinx
import numpy as np

mesh = dolfinx.mesh.create_unit_square(MPI.COMM_WORLD, 10, 10)

geom_imap = mesh.geometry.index_map()

local_range = geom_imap.local_range

num_nodes_local = local_range[1] - local_range[0]

nodes = mesh.geometry.x.reshape(-1, 3)[:num_nodes_local, :]

all_nodes = mesh.comm.gather(nodes, root=0)
if mesh.comm.rank == 0:
    all_nodes = np.vstack(all_nodes)
    print(all_nodes.shape)

num_cells_local = mesh.topology.index_map(mesh.topology.dim).size_local
connectivity = mesh.geometry.dofmap[:num_cells_local, :]
global_connectivity = geom_imap.local_to_global(connectivity.flatten()).reshape(-1, connectivity.shape[1])

all_connectivity = mesh.comm.gather(global_connectivity, root=0)
if mesh.comm.rank == 0:
    all_connectivity = np.vstack(all_connectivity)
    print(all_connectivity.shape)