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

.. only:: html

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

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

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

.. _sphx_glr_gallery_examples_verifications_make_cantilever_discrete.py:


Cantilever discrete design
##########################

.. GENERATED FROM PYTHON SOURCE LINES 8-12

This third example is a new variation of the cantilever design problem with a three fields optimization, i.e. with the raw, the filtered and the projected density parameter fields.
 Projected density parameter field is obtained by projecting the filtered field using a smooth Heaviside function.
 This strategy could be use to obtain discrete 0-1 design at the end of the optimization by carring a multi-steps optimization process and increasing the steepness of the smooth Heaviside function at each step.
 We first create the optimization problem

.. GENERATED FROM PYTHON SOURCE LINES 12-49

.. code-block:: Python


    import numpy as np
                                  
    from HydrOpTop.Functions.verification import Mechanical_Compliance
    from HydrOpTop.Functions import Volume_Percentage
    from HydrOpTop.Materials import SIMP
    from HydrOpTop.Filters import Density_Filter, Volume_Preserving_Heaviside_Filter
    from HydrOpTop.Crafter import Steady_State_Crafter
    from HydrOpTop.Solvers import Linear_Elasticity_2D

    #create PFLOTRAN simulation object
    sim = Linear_Elasticity_2D("cantilever")

    #get cell ids in the region to optimize and parametrize permeability
    #same name than in pflotran input file
    perm = SIMP(cell_ids_to_parametrize="all", property_name="YOUNG_MODULUS", bounds=[0, 2000], power=3)

    #define cost function
    cf = Mechanical_Compliance(ids_to_consider="everywhere")

    #define maximum volume constrains
    max_vol = Volume_Percentage("parametrized_cell")
    max_vol.constraint_tol = 0.5

    #define filter
    dfilter = Density_Filter(0.3)
    hfilter = Volume_Preserving_Heaviside_Filter(0.5, 1, max_vol)

    #craft optimization problem
    #i.e. create function to optimize, initiate IO array in classes...
    crafted_problem = Steady_State_Crafter(cf, sim, [perm], [max_vol], filters=[dfilter, hfilter]) #apply first density filter (dfilter) and then the Heaviside filter (hfilter)
    crafted_problem.IO.output_every_iteration(2)
    crafted_problem.IO.define_output_format("vtu")

    #initialize optimizer
    p = np.zeros(crafted_problem.get_problem_size(),dtype='f8') + 0.2


.. GENERATED FROM PYTHON SOURCE LINES 50-52

The optimization is carried out in several step, starting from a smooth Heavyside density filter and increasing the steepness parameter.
As this can be difficult to converge for high step parameter, we increase it gradually to to reach a discrete distribution of material.

.. GENERATED FROM PYTHON SOURCE LINES 52-70

.. code-block:: Python


    p_opt = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                     max_it=50, ftol=0.0001, initial_guess=p)
    hfilter.update_stepness(2)
    p_opt = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                     max_it=20, initial_guess=p_opt.p_opt)
    hfilter.update_stepness(4)
    p_opt = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                     max_it=10, initial_guess=p_opt.p_opt)
    hfilter.update_stepness(8)
    p_opt = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                     max_it=10, initial_guess=p_opt.p_opt)
    hfilter.update_stepness(20)
    p_opt = crafted_problem.optimize(optimizer="nlopt-mma", action="minimize", 
                                     max_it=5, initial_guess=p_opt.p_opt)

    crafted_problem.IO.write_fields_to_file([p_opt.p_opt_filtered], "./out.vtu", ["Filtered_density"])
    crafted_problem.IO.plot_convergence_history()


.. _sphx_glr_download_gallery_examples_verifications_make_cantilever_discrete.py:

.. only:: html

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

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

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

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

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


.. only:: html

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

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