L-shape mesh generation with right element

mesh
1

Hi,
I would like to construct an L-shape domain with ‘right’ element( this is the aim).

To do so, I have constructed two rectangles and would like to add them together. How can I implement this?

from dolfin import *
import numpy as np
import matplotlib.pyplot as plt
from mshr import *

num_elem = 4
mesh1 = RectangleMesh(Point(0, 0), Point(1, 0.5), num_elem, num_elem)
plot(mesh1)
plt.show()
mesh2 = RectangleMesh(Point(0., 0.5), Point(0.5, 1), int(num_elem/2), int(num_elem/2))
plot(mesh2)
plt.show()
domain = mesh1 + mesh2

2

I don’t get what you mean by “right” element. But, for what its worth, the way to go would be something like:

from mshr import Rectangle, generate_mesh
from dolfin import *

rect1 = Rectangle(Point(0, 0), Point(0.5, 1))
rect2 = Rectangle(Point(0, 0), Point(1, 0.5))
mesh = generate_mesh(rect1 + rect2, 50)

Note that mshr is no longer actively maintained

1 Like
3

Thank you for the reply.

what I mean is that I need my elements to be ‘right’ triangle (attached) not as polygons as in the case of Rectangle. Figure_1

4

Use gmsh for this with the Transfinite Surface command.

2 Likes
5

Another ad-hoc approach would be to generate a coarse mesh and then successively refine it.

rect1 = Rectangle(Point(0, 0), Point(0.5, 1))
rect2 = Rectangle(Point(0, 0), Point(1, 0.5))
mesh = generate_mesh(rect1 + rect2, 1)
num_refinements = 3
for i in range(num_refinements):
    mesh = refine(mesh)
6

Thank you for the reply and help.

However, I just need a right triangle element (attached fig)
Figure_1 )
and what refine produces is a crossed mesh ( i…e right/left attached).
Figure_2

7

You can build your mesh using the MeshEditor.
See for instance: Bitbucket

2 Likes
8

Thank you for your reply.
Can you provide me with a small example on how to construct as simple mesh with MeshEditor?

9

The link above showed how to make it for a single cell. In this post I’ve now added a simple L-shape mesh with “left” diagonals.

import matplotlib.pyplot as plt
from dolfin import *
import numpy
# Create mesh object and open editor
mesh = Mesh()
editor = MeshEditor()
topological_dim = 2
geometrical_dim = 2
num_local_vertices = 8
num_global_vertices = num_local_vertices  # True if run in serial
num_local_cells = 6
num_global_cells = num_local_cells
editor.open(mesh, "triangle", topological_dim, geometrical_dim)
editor.init_vertices_global(num_local_vertices, num_global_vertices)
editor.init_cells_global(num_local_cells, num_global_cells)

# Add vertices
editor.add_vertex(0, numpy.array([0.0, 0.0], dtype='float'))
editor.add_vertex(1, numpy.array([1.0, 0.0], dtype='float'))
editor.add_vertex(2, numpy.array([0.0, 1.0], dtype='float'))
editor.add_vertex(3, numpy.array([1.0, 1.0], dtype='float'))
editor.add_vertex(4, numpy.array([0.0, 2.0], dtype='float'))
editor.add_vertex(5, numpy.array([1.0, 2.0], dtype='float'))
editor.add_vertex(6, numpy.array([3.0, 0.0], dtype='float'))
editor.add_vertex(7, numpy.array([3.0, 1.0], dtype='float'))
# Add cell
editor.add_cell(0, numpy.array([0, 1, 2], dtype='uint'))
editor.add_cell(1, numpy.array([1, 2, 3], dtype='uint'))
editor.add_cell(2, numpy.array([2, 3, 4], dtype='uint'))
editor.add_cell(3, numpy.array([3, 4, 5], dtype='uint'))
editor.add_cell(4, numpy.array([1, 6, 3], dtype='uint'))
editor.add_cell(5, numpy.array([6, 7, 3], dtype='uint'))
# Close editor
editor.close()

plot(mesh, color="r")
plt.savefig("mesh.png")
1 Like
10

THANK YOU… This was extremely helpful.