Periodic boundary conditions between non conforming subdomamains and different function spaces

JLorenteMacias · November 26, 2025, 11:53am

Dear community,

I’m interested in solving a problem over a domain \Omega = \Omega_1 \cup \Omega_2 \cup \Omega_3. This creates a boundary \Gamma=\Gamma_L \cup \Gamma_T \cup \Gamma_R \cup \Gamma_B and some shared interfaces \Gamma_I = \Gamma_{I_{1}} \cup \Gamma_{I_{2}} (see image below).

I want to impose periodic boundary conditions between \Gamma_B and \Gamma_T. I have seen that dolfinx_mpc can handle this, but the tricky part in my problem is that \Omega_1 and \Omega_3 are disjoint.

I’ve seen a similar problem here Create constraint between two bodies that are not in contact, but even if subdomains are disjoint there as well, they use a global Function Space. In my case, I have a function space V1 for \Omega_1, V2 for \Omega_2 and V3 for \Omega_3.

Does anybody know if dolfinx_mpc can still handle this?

I can post a minimal code if needed, but I wanted to know first if this is the right direction.

Thanks in advance.

dokken · November 26, 2025, 12:04pm

For DOLFINx MPC to work, you would have to concatenate the three domains into a single domain.

This is for instance done for non-conforming cubes in:

github.com/jorgensd/dolfinx_mpc

python/demos/create_and_export_mesh.py

main


      
          # Stack the two meshes in one mesh
          r_matrix = _utils.rotation_matrix([0, 0, 1], theta)
          _points = np.vstack([mesh0.geometry.x, mesh1.geometry.x])
          _points = np.dot(r_matrix, _points.T)
          _points = _points[:2, :].T
          points: npt.NDArray[np.floating] = _points.astype(default_real_type)
          
          # Transform topology info into geometry info
          tdim0 = mesh0.topology.dim
          num_cells0 = mesh0.topology.index_map(tdim0).size_local
          mesh0.topology.create_connectivity(tdim0, tdim0)
          cells0 = _cpp.mesh.entities_to_geometry(mesh0._cpp_object, tdim0, np.arange(num_cells0, dtype=np.int32), False)
          tdim1 = mesh1.topology.dim
          num_cells1 = mesh1.topology.index_map(tdim1).size_local
          mesh1.topology.create_connectivity(tdim1, tdim1)
          cells1 = _cpp.mesh.entities_to_geometry(mesh1._cpp_object, tdim1, np.arange(num_cells1, dtype=np.int32), False)
          cells1 += mesh0.geometry.x.shape[0]
          
          cells = np.vstack([cells0, cells1]).astype(np.int64)
          domain = ufl.Mesh(element("Lagrange", ct.name, 1, shape=(points.shape[1],)))
          mesh = _mesh.create_mesh(comm=MPI.COMM_SELF, cells=cells, x=points, e=domain)

that is used for non-conforming contact between two bodies in:

github.com/jorgensd/dolfinx_mpc

python/demos/demo_contact_2D.py

main

# Copyright (C) 2020 Jørgen S. Dokken
#
# This file is part of DOLFINX_MPC
#
# SPDX-License-Identifier:    MIT
#
# This demo demonstrates how to solve a contact problem between
# two stacked cubes.
# The bottom cube is fixed at the bottom surface
# The top cube has a force applied normal to its to surface.
# A slip condition is implemented at the interface of the cube.
# Additional constraints to avoid tangential movement is
# added to the to left corner of the top cube.
from __future__ import annotations

import warnings
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser
from pathlib import Path

from mpi4py import MPI

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Periodic boundary conditions between non conforming subdomamains and different function spaces

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