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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_dimension_reduction_pod_DiffusionEquation.py>`
        to download the full example code or to run this example in your browser via Binder

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

.. _sphx_glr_auto_examples_dimension_reduction_pod_DiffusionEquation.py:


Diffusion Equation File
========================

.. GENERATED FROM PYTHON SOURCE LINES 8-38

.. code-block:: default

    import numpy as np
    def diffusion(w, h, dx, dy, D, Tcool, Thot, r, cx, cy, nsteps):
        nx, ny = int(w/dx), int(h/dy)

        dx2, dy2 = dx*dx, dy*dy
        dt = dx2 * dy2 / (2 * D * (dx2 + dy2))

        u0 = Tcool * np.ones((nx, ny))
        u = u0.copy()

        r2 = r**2
        for i in range(nx):
            for j in range(ny):
                p2 = (i*dx-cx)**2 + (j*dy-cy)**2
                if p2 < r2:
                    u0[i,j] = Thot

        def do_timestep(u0, u):
            # Propagate with forward-difference in time, central-difference in space
            u[1:-1, 1:-1] = u0[1:-1, 1:-1] + D * dt * (
                  (u0[2:, 1:-1] - 2*u0[1:-1, 1:-1] + u0[:-2, 1:-1])/dx2
                  + (u0[1:-1, 2:] - 2*u0[1:-1, 1:-1] + u0[1:-1, :-2])/dy2 )

            u0 = u.copy()
            return u0, u

        u_f = []
        for m in range(nsteps):
            u0, u = do_timestep(u0, u)
            u_f.append(u0)
        return u_f

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

   **Total running time of the script:** ( 0 minutes  0.000 seconds)


.. _sphx_glr_download_auto_examples_dimension_reduction_pod_DiffusionEquation.py:

.. only:: html

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


    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/SURGroup/UQpy/master?urlpath=lab/tree/notebooks/auto_examples/dimension_reduction/pod/DiffusionEquation.ipynb
        :alt: Launch binder
        :width: 150 px



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

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

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

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


.. only:: html

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

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