.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples_gallery/advanced_pdes/pde_brusselator_class.py"
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.. only:: html

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

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

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

.. _sphx_glr_examples_gallery_advanced_pdes_pde_brusselator_class.py:


Brusselator - Using custom class
================================

This example implements the `Brusselator
<https://en.wikipedia.org/wiki/Brusselator>`_ with spatial coupling,

.. math::

    \partial_t u &= D_0 \nabla^2 u + a - (1 + b) u + v u^2 \\
    \partial_t v &= D_1 \nabla^2 v + b u - v u^2

Here, :math:`D_0` and :math:`D_1` are the respective diffusivity and the
parameters :math:`a` and :math:`b` are related to reaction rates.

Note that the PDE can also be implemented using the :class:`~pde.pdes.pde.PDE`
class; see :doc:`the example <../simple_pdes/pde_brusselator_expression>`. However, that
implementation is less flexible and might be more difficult to extend later.

.. GENERATED FROM PYTHON SOURCE LINES 20-78



.. image-sg:: /examples_gallery/advanced_pdes/images/sphx_glr_pde_brusselator_class_001.png
   :alt: Time: 20
   :srcset: /examples_gallery/advanced_pdes/images/sphx_glr_pde_brusselator_class_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import numpy as np

    from pde import FieldCollection, PDEBase, PlotTracker, ScalarField, UnitGrid


    class BrusselatorPDE(PDEBase):
        """Brusselator with diffusive mobility."""

        def __init__(self, a=1, b=3, diffusivity=None, bc="auto_periodic_neumann"):
            super().__init__()
            self.a = a
            self.b = b
            self.diffusivity = [1, 0.1] if diffusivity is None else diffusivity
            self.bc = bc  # boundary condition

        def get_initial_state(self, grid):
            """Prepare a useful initial state."""
            u = ScalarField(grid, self.a, label="Field $u$")
            v = self.b / self.a + 0.1 * ScalarField.random_normal(grid, label="Field $v$")
            return FieldCollection([u, v])

        def evolution_rate(self, state, t=0):
            """Pure python implementation of the PDE."""
            u, v = state
            rhs = state.copy()
            d0, d1 = self.diffusivity
            rhs[0] = d0 * u.laplace(self.bc) + self.a - (self.b + 1) * u + u**2 * v
            rhs[1] = d1 * v.laplace(self.bc) + self.b * u - u**2 * v
            return rhs

        def make_evolution_rate(self, state, backend):
            """Compilable implementation of the PDE."""
            d0, d1 = self.diffusivity
            a, b = self.a, self.b
            laplace = state.grid.make_operator(
                "laplace", bc=self.bc, backend=backend, dtype=state.dtype
            )

            def pde_rhs(state_data, t):
                u = state_data[0]
                v = state_data[1]

                rate_u = d0 * laplace(u) + a - (1 + b) * u + v * u**2
                rate_v = d1 * laplace(v) + b * u - v * u**2
                return np.stack((rate_u, rate_v))

            return pde_rhs


    # initialize state
    grid = UnitGrid([64, 64])
    eq = BrusselatorPDE(diffusivity=[1, 0.1])
    state = eq.get_initial_state(grid)

    # simulate the pde
    tracker = PlotTracker(interrupts=1, plot_args={"kind": "merged", "vmin": 0, "vmax": 5})
    sol = eq.solve(state, t_range=20, dt=1e-3, tracker=tracker)


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

   **Total running time of the script:** (0 minutes 8.496 seconds)


.. _sphx_glr_download_examples_gallery_advanced_pdes_pde_brusselator_class.py:

.. only:: html

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

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

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

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

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

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

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