Locate_entities_boundary & embed gmsh boundaries?

General
1

Hello,

I’m interested in solving a problem on a mesh similar to:

image
image695×701 9.74 KB

It consists basically of a square domain where is added an embedded line where boundary conditions are to be applied.

The mesh is created with gmsh and converted to dolfinx with the following script:

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
import dolfinx
from mpi4py import MPI
import numpy as np
import gmsh

#
#======================
# Create the gmsh mesh
#======================
#
gmsh.initialize()
gmsh.model.add("t1")

s1_lower_left  = gmsh.model.geo.addPoint(0.0, 0.0, 0, 0.4)
s1_lower_right = gmsh.model.geo.addPoint(1.0, 0.0, 0, 0.4)
s1_upper_right = gmsh.model.geo.addPoint(1.0, 1.0, 0, 0.4)
s1_upper_left  = gmsh.model.geo.addPoint(0.0, 1.0, 0, 0.4)

s1_left  = gmsh.model.geo.addLine(s1_lower_left, s1_upper_left)
s1_right = gmsh.model.geo.addLine(s1_lower_right, s1_upper_right)
s1_lower = gmsh.model.geo.addLine(s1_lower_left, s1_lower_right)
s1_upper = gmsh.model.geo.addLine(s1_upper_left, s1_upper_right)

s1_surface = gmsh.model.geo.addPlaneSurface([gmsh.model.geo.addCurveLoop([-s1_left, s1_lower, s1_right, -s1_upper])])

embed_left_point = gmsh.model.geo.addPoint(0.5, 0.5, 0, 0.4)
embed_line  = gmsh.model.geo.addLine(embed_left_point, s1_upper_right)


gmsh.model.geo.synchronize()
gmsh.model.mesh.embed(1, [embed_line], 2, s1_surface)
gmsh.model.geo.synchronize()

MARKER = 2
gmsh.model.addPhysicalGroup(2, [s1_surface], 1)
gmsh.model.addPhysicalGroup(1, [s1_left, s1_lower, s1_right, s1_upper, embed_line], MARKER)

gmsh.model.mesh.generate(2)
#
#=========================
# Convert to dolfinx mesh
#=========================
#
msh, cell_tags, facet_tags = dolfinx.io.gmshio.model_to_mesh(gmsh.model, comm=MPI.COMM_WORLD, rank=0, gdim=2)

bdry = dolfinx.mesh.locate_entities_boundary(msh, 1, lambda x: np.full_like(x[0], 1, dtype=np.int8))
print('Number of tags: ',facet_tags.values.size)
print('Number of boundary ',bdry.size)

# gmsh.fltk.run()
gmsh.finalize()

The output of this script is:

Number of tags:  14
Number of boundary  12

This shows that actually locate_entities_boundary does not locate the embedded boundary. This is quite a problem for me because I usually use locate_dofs_topological(function_space, 1, bdry[facet_tags==MARKER]) to impose boundary conditions. How can this be done for embedded boundary conditions?

Best,

Lucas

2

It is quite natural that the line that is inside the mesh is not found by locate_entities_boundary, as it is not on the boundary, it is shared between two cells.

As you make the mesh with gmsh, you should be able to simply use the facet_tags directly in locate_dofs_topological. I.e facet_tags.find(1) should give you all the marked facets from

which includes the embedded line.

3

Thanks Dokkfen, that’s the solution I needed.