Built-in meshes =============== This demo is implemented in a single Python file, :download:demo_built-in-meshes.py, and demonstrates use of the built-in meshes in DOLFIN. This demo illustrates: * How to define some of the different built-in meshes in DOLFIN Problem definition ------------------ The demo focuses on the built-in meshes. We will look at the following meshes: * :py:class:UnitIntervalMesh  * :py:class:UnitSquareMesh  * :py:class:RectangleMesh  * :py:class:UnitCubeMesh  * :py:class:BoxMesh  Implementation -------------- First, the :py:mod:dolfin module is imported:: from dolfin import * import matplotlib.pyplot as plt The first mesh we make is a mesh over the unit interval :math:(0,1). :py:class:UnitIntervalMesh  takes the number of intervals :math:(n_x) as input argument, and the total number of vertices is therefore :math:(n_x+1). :: mesh = UnitIntervalMesh(10) print("Plotting a UnitIntervalMesh") plt.figure() plot(mesh, title="Unit interval") This produces a mesh looking as follows: .. image:: unitintervalmesh.png :scale: 75 % We then make our first version of a mesh on the unit square :math:[0,1] \times [0,1]. We must give the number of cells in the horizontal and vertical directions as the first two arguments to :py:class:UnitSquareMesh . There is a third optional argument that indicates the direction of the diagonals. This can be set to "left", "right", "right/left", "left/right", or "crossed". We can also omit this argument and thereby use the default direction "right". :: mesh = UnitSquareMesh(10, 10) print("Plotting a UnitSquareMesh") plt.figure() plot(mesh, title="Unit square") .. image:: unitsquaremesh.png :scale: 75 % Our second version of a mesh on the unit square has diagonals to the left, the third version has crossed diagonals and our final version has diagonals to both left and right:: mesh = UnitSquareMesh(10, 10, "left") print("Plotting a UnitSquareMesh") plot(mesh, title="Unit square (left)") mesh = UnitSquareMesh(10, 10, "crossed") print("Plotting a UnitSquareMesh") plot(mesh, title="Unit square (crossed)") mesh = UnitSquareMesh(10, 10, "right/left") print("Plotting a UnitSquareMesh") plt.figure() plot(mesh, title="Unit square (right/left)") .. image:: unitsquaremesh_left.png :scale: 65 % .. image:: unitsquaremesh_crossed.png :scale: 65 % .. image:: unitsquaremesh_left_right.png :scale: 65 % The class :py:class:RectangleMesh  creates a mesh of a 2D rectangle spanned by two points (opposing corners) of the rectangle. Three additional arguments specify the number of divisions in the :math:x- and :math:y-directions, and as above the direction of the diagonals is given as a final optional argument ("left", "right", "left/right", or "crossed"). In the first mesh we use the default direction ("right") of the diagonal, and in the second mesh we use diagonals to both left and right. :: mesh = RectangleMesh(Point(0.0, 0.0), Point(10.0, 4.0), 10, 10) print("Plotting a RectangleMesh") plt.figure() plot(mesh, title="Rectangle") mesh = RectangleMesh(Point(-3.0, 2.0), Point(7.0, 6.0), 10, 10, "right/left") print("Plotting a RectangleMesh") plt.figure() plot(mesh, title="Rectangle (right/left)") .. image:: rectanglemesh.png :scale: 75 % .. image:: rectanglemesh_left_right.png :scale: 75 % To make a mesh of the 3D unit cube :math:[0,1] \times [0,1] \times [0,1], we use :py:class:UnitCubeMesh . :py:class:UnitCubeMesh  takes the number of cells in the :math:x-, :math:y- and :math:z-direction as the only three arguments. :: mesh = UnitCubeMesh(10, 10, 10) print("Plotting a UnitCubeMesh") plt.figure() plot(mesh, title="Unit cube") .. image:: unitcubemesh.png :scale: 75 % Finally we will demonstrate a mesh on a rectangular prism in 3D. The prism is specified by two points (opposing corners) of the prism. Three additional arguments specify the number of divisions in the :math:x-, :math:y- and :math:z-directions. Meshes for more complex geometries may be created using the mshr library, which functions as a plugin to DOLFIN, providing support for Constructive Solid Geometry (CSG) and mesh generation. For more details, refer to the mshr documentation. :: mesh = BoxMesh(Point(0.0, 0.0, 0.0), Point(10.0, 4.0, 2.0), 10, 10, 10) print("Plotting a BoxMesh") plt.figure() plot(mesh, title="Box") plt.show() .. image:: boxmesh.png :scale: 75 %