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Operators
=========

Numerical solutions to differential equations using the finite volume
method require discrete operators. These include averaging operators
and differential operators. Averaging operators are used when a
variable living on some part of the mesh (e.g. nodes, centers, edges or
faces) must be approximated at other locations. Differential operators
include the gradient, divergence, curl and scalar Laplacian.

The discrete operators are properties of each mesh class (*tensor mesh*,
*tree mesh*, *curvilinear mesh*). An operator is only constructed when
called. Since each mesh type has a similar API, the operators can be
called using the same syntax.

To learn about discrete operators, we have provided a set
of tutorials. These tutorials aim to teach the user:

	- how to construct averaging and differential operators from a mesh
	- how to apply the discrete operators to discrete variables
	- how to impose boundary conditions using differential operators
	- how discrete differential operators preserve vector calculus identities






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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Averaging matricies are used when a discrete variable living on some part of the mesh (e.g. nodes, centers, edges or faces) must be approximated at other locations. Averaging matricies are sparse and exist for 1D, 2D and 3D meshes. For each mesh class (Tensor mesh, Tree mesh, Curvilinear mesh), the set of averaging matricies are properties that are only constructed when called.">

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  .. image:: /tutorials/operators/images/thumb/sphx_glr_1_averaging_thumb.png
    :alt:

  :ref:`sphx_glr_tutorials_operators_1_averaging.py`

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      <div class="sphx-glr-thumbnail-title">Averaging Matricies</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="For discretized quantities living on a mesh, sparse matricies can be used to approximate the following differential operators:">

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  .. image:: /tutorials/operators/images/thumb/sphx_glr_2_differential_thumb.png
    :alt:

  :ref:`sphx_glr_tutorials_operators_2_differential.py`

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      <div class="sphx-glr-thumbnail-title">Differential Operators</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /tutorials/operators/1_averaging
   /tutorials/operators/2_differential


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  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: operators_python.zip </tutorials/operators/operators_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: operators_jupyter.zip </tutorials/operators/operators_jupyter.zip>`


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

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