.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "tutorials/mesh_generation/1_mesh_overview.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_tutorials_mesh_generation_1_mesh_overview.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_tutorials_mesh_generation_1_mesh_overview.py:


Overview of Mesh Types
======================

Here we provide an overview of mesh types and define some terminology.
Separate tutorials have been provided for each mesh type.

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.. code-block:: Python


    import numpy as np
    import discretize
    import matplotlib.pyplot as plt








.. GENERATED FROM PYTHON SOURCE LINES 15-28

General Categories of Meshes
----------------------------

The three main types of meshes in discretize are

   - **Tensor meshes** (:class:`discretize.TensorMesh`); which includes **cylindrical meshes** (:class:`discretize.CylindricalMesh`)

   - **Tree meshes** (:class:`discretize.TreeMesh`): also referred to as QuadTree or OcTree meshes

   - **Curvilinear meshes** (:class:`discretize.CurvilinearMesh`): also referred to as logically rectangular non-orthogonal

Examples for each mesh type are shown below.


.. GENERATED FROM PYTHON SOURCE LINES 28-63

.. code-block:: Python


    ncx = 16  # number of cells in the x-direction
    ncy = 16  # number of cells in the y-direction

    # create a tensor mesh
    tensor_mesh = discretize.TensorMesh([ncx, ncy])

    # create a tree mesh and refine some of the cells
    tree_mesh = discretize.TreeMesh([ncx, ncy])


    def refine(cell):
        if np.sqrt(((np.r_[cell.center] - 0.5) ** 2).sum()) < 0.2:
            return 4
        return 2


    tree_mesh.refine(refine)

    # create a curvilinear mesh
    curvi_mesh = discretize.CurvilinearMesh(
        discretize.utils.example_curvilinear_grid([ncx, ncy], "rotate")
    )

    # Plot
    fig, axes = plt.subplots(1, 3, figsize=(14.5, 4))
    tensor_mesh.plot_grid(ax=axes[0])
    axes[0].set_title("TensorMesh")

    tree_mesh.plot_grid(ax=axes[1])
    axes[1].set_title("TreeMesh")

    curvi_mesh.plot_grid(ax=axes[2])
    axes[2].set_title("CurvilinearMesh")




.. image-sg:: /tutorials/mesh_generation/images/sphx_glr_1_mesh_overview_001.png
   :alt: TensorMesh, TreeMesh, CurvilinearMesh
   :srcset: /tutorials/mesh_generation/images/sphx_glr_1_mesh_overview_001.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, 'CurvilinearMesh')



.. GENERATED FROM PYTHON SOURCE LINES 64-77

Variable Locations and Terminology
----------------------------------

When solving differential equations on a numerical grid, variables can be
defined on:

   - nodes
   - cell centers
   - cell faces
   - cell edges

Below we show an example for a 2D tensor mesh.


.. GENERATED FROM PYTHON SOURCE LINES 77-96

.. code-block:: Python


    hx = np.r_[3, 1, 1, 3]
    hy = np.r_[3, 2, 1, 1, 1, 1, 2, 3]
    tensor_mesh2 = discretize.TensorMesh([hx, hy])

    # Plot
    fig, axes2 = plt.subplots(1, 3, figsize=(14.5, 5))
    tensor_mesh2.plot_grid(ax=axes2[0], nodes=True, centers=True)
    axes2[0].legend(("Nodes", "Centers"))
    axes2[0].set_title("Nodes and cell centers")

    tensor_mesh2.plot_grid(ax=axes2[1], edges=True)
    axes2[1].legend(("X-edges", "Y-edges"))
    axes2[1].set_title("Cell edges")

    tensor_mesh2.plot_grid(ax=axes2[2], faces=True)
    axes2[2].legend(("X-faces", "Y-faces"))
    axes2[2].set_title("Cell faces")




.. image-sg:: /tutorials/mesh_generation/images/sphx_glr_1_mesh_overview_002.png
   :alt: Nodes and cell centers, Cell edges, Cell faces
   :srcset: /tutorials/mesh_generation/images/sphx_glr_1_mesh_overview_002.png
   :class: sphx-glr-single-img


.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    Text(0.5, 1.0, 'Cell faces')



.. GENERATED FROM PYTHON SOURCE LINES 97-101

Note that we define X-edges as being edges that lie parallel to the x-axis.
And we define X-faces as being faces whose normal lies parallel to the
axis. In 3D, the difference between edges and faces is more obvious.



.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.590 seconds)


.. _sphx_glr_download_tutorials_mesh_generation_1_mesh_overview.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: 1_mesh_overview.ipynb <1_mesh_overview.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: 1_mesh_overview.py <1_mesh_overview.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: 1_mesh_overview.zip <1_mesh_overview.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_