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

.. only:: html

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

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

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

.. _sphx_glr_examples_plot_quadtree_divergence.py:


QuadTree: FaceDiv
=================

For a tree mesh, there needs to be special attention taken for the hanging
faces to achieve second order convergence for the divergence operator.
Although the divergence cannot be constructed through Kronecker product
operations, the initial steps are exactly the same for calculating the
stencil, volumes, and areas. This yields a divergence defined for every
cell in the mesh using all faces. There is, however, redundant information
when hanging faces are included.

.. GENERATED FROM PYTHON SOURCE LINES 13-54



.. image-sg:: /examples/images/sphx_glr_plot_quadtree_divergence_001.png
   :alt: Simple QuadTree Mesh, Face Divergence
   :srcset: /examples/images/sphx_glr_plot_quadtree_divergence_001.png
   :class: sphx-glr-single-img





.. code-block:: default

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


    def run(plotIt=True, n=60):
        M = discretize.TreeMesh([[(1, 16)], [(1, 16)]], levels=4)
        M.insert_cells(np.array([5.0, 5.0]), np.array([3]))
        M.number()

        if plotIt:
            fig, axes = plt.subplots(2, 1, figsize=(10, 10))

            M.plot_grid(centers=True, nodes=False, ax=axes[0])
            axes[0].axis("off")
            axes[0].set_title("Simple QuadTree Mesh")
            axes[0].set_xlim([-1, 17])
            axes[0].set_ylim([-1, 17])

            for ii, loc in zip(range(M.nC), M.gridCC):
                axes[0].text(loc[0] + 0.2, loc[1], "{0:d}".format(ii), color="r")

            axes[0].plot(M.gridFx[:, 0], M.gridFx[:, 1], "g>")
            for ii, loc in zip(range(M.nFx), M.gridFx):
                axes[0].text(loc[0] + 0.2, loc[1], "{0:d}".format(ii), color="g")

            axes[0].plot(M.gridFy[:, 0], M.gridFy[:, 1], "m^")
            for ii, loc in zip(range(M.nFy), M.gridFy):
                axes[0].text(
                    loc[0] + 0.2, loc[1] + 0.2, "{0:d}".format((ii + M.nFx)), color="m"
                )

            axes[1].spy(M.face_divergence)
            axes[1].set_title("Face Divergence")
            axes[1].set_ylabel("Cell Number")
            axes[1].set_xlabel("Face Number")


    if __name__ == "__main__":
        run()
        plt.show()


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

   **Total running time of the script:** (0 minutes 0.262 seconds)


.. _sphx_glr_download_examples_plot_quadtree_divergence.py:

.. only:: html

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




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

      :download:`Download Python source code: plot_quadtree_divergence.py <plot_quadtree_divergence.py>`

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

      :download:`Download Jupyter notebook: plot_quadtree_divergence.ipynb <plot_quadtree_divergence.ipynb>`


.. only:: html

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

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