.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples/01-simple/poison_eq.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_examples_01-simple_poison_eq.py>`
        to download the full example code.

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

.. _sphx_glr_examples_01-simple_poison_eq.py:


Define and solve user equation
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Basic example that show how to define the poisson equation and
how to solve it with Dirichlet boundary conditions.

.. GENERATED FROM PYTHON SOURCE LINES 7-10

.. code-block:: Python


    import fedoo as fd








.. GENERATED FROM PYTHON SOURCE LINES 11-13

Define a modeling space and add a variable "U" to this space
A "2D" problem include by default the coordinates "X" and "Y".

.. GENERATED FROM PYTHON SOURCE LINES 13-16

.. code-block:: Python

    space = fd.ModelingSpace("2D")
    U = space.new_variable("U")








.. GENERATED FROM PYTHON SOURCE LINES 17-23

Set the equation to solve on a weak form.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
The space.derivative or space.variable functions create a differatial equation that we
can combine with the +, - and * operators to build the weak form.
the virtual properties set the variable as virtuals
(in the sense of weak equations)

.. GENERATED FROM PYTHON SOURCE LINES 23-28

.. code-block:: Python

    dU_dX = space.derivative("U", "X")
    dU_dY = space.derivative("U", "Y")

    wf = fd.WeakForm(dU_dX.virtual * dU_dX + dU_dY.virtual * dU_dY, name="Poisson Equation")








.. GENERATED FROM PYTHON SOURCE LINES 29-30

Define the integration domain (mesh)

.. GENERATED FROM PYTHON SOURCE LINES 30-32

.. code-block:: Python

    mesh = fd.mesh.rectangle_mesh()








.. GENERATED FROM PYTHON SOURCE LINES 33-35

Assembly the global matrix, define a linear problem,
add boundary conditions and solve the problem

.. GENERATED FROM PYTHON SOURCE LINES 35-45

.. code-block:: Python

    fd.Assembly.create(wf, mesh, name="assembly")

    pb = fd.problem.Linear("assembly")
    pb.bc.add("Dirichlet", "left", "U", 0)
    pb.bc.add("Dirichlet", "right", "U", 1)

    pb.solve()

    res = pb.get_results("assembly", ["U"])
    res.plot("U")




.. image-sg:: /examples/01-simple/images/sphx_glr_poison_eq_001.png
   :alt: poison eq
   :srcset: /examples/01-simple/images/sphx_glr_poison_eq_001.png
   :class: sphx-glr-single-img








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

   **Total running time of the script:** (0 minutes 0.271 seconds)


.. _sphx_glr_download_examples_01-simple_poison_eq.py:

.. only:: html

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

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

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

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

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

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

      :download:`Download zipped: poison_eq.zip <poison_eq.zip>`


.. only:: html

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

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