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

.. only:: html

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

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

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

.. _sphx_glr_gallery_verification_example_verify_patch_test.py:


Irons constant-strain patch test
================================

The canonical FE consistency test: a 2×2×2 hex patch with an
interior node displaced from its regular position, subjected to
boundary displacements :math:`u = \varepsilon_0\, x` consistent
with a uniform axial strain field, must recover
:math:`\varepsilon = \varepsilon_0` everywhere to **machine
precision**.

Reference: Irons, B. M. and Razzaque, A. (1972) "Experience with
the patch test for convergence of finite elements," *The
Mathematical Foundations of the Finite Element Method*, pp.
557-587.

A discretisation that fails this test cannot pass the inf-sup /
consistency conditions and therefore cannot converge at the
optimal rate.  A pass at machine precision says the element
kernel is wiring :math:`B`, :math:`D`, and the isoparametric
mapping correctly under non-trivial geometry.

.. GENERATED FROM PYTHON SOURCE LINES 23-31

.. code-block:: Python


    from __future__ import annotations

    import numpy as np
    import pyvista as pv

    from femorph_solver.validation.problems import IronsPatchTest








.. GENERATED FROM PYTHON SOURCE LINES 32-33

Problem statement

.. GENERATED FROM PYTHON SOURCE LINES 33-41

.. code-block:: Python


    problem = IronsPatchTest()
    pv_ = problem.published_values[0]
    print(f"{problem.name}: {problem.description}")
    print(f"\n  source : {pv_.source}")
    print(f"  formula: {pv_.formula}")
    print(f"  target : {pv_.value} (tolerance {pv_.tolerance:.0e})")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none

    patch_test: Irons constant-strain patch test: prescribed linear boundary displacement must reproduce a uniform strain to machine precision.

      source : Irons & Razzaque 1972
      formula: max_e |eps_xx^h(x_e) - eps0| == 0 (machine precision)
      target : 0.0 (tolerance 1e-09)




.. GENERATED FROM PYTHON SOURCE LINES 42-43

Run the check — single-shot ``validate()``

.. GENERATED FROM PYTHON SOURCE LINES 43-49

.. code-block:: Python


    results = problem.validate()
    r = results[0]
    print(f"\n  computed max_strain_error: {r.computed:.3e}")
    print(f"  passes tolerance          : {r.passed}")





.. rst-class:: sphx-glr-script-out

 .. code-block:: none


      computed max_strain_error: 8.132e-20
      passes tolerance          : True




.. GENERATED FROM PYTHON SOURCE LINES 50-56

Figure — the distorted patch
----------------------------
The validation's ``build_model`` offsets the single interior
node by 10 % of the edge length so the isoparametric mapping
is non-trivial; rendering the resulting mesh is a nice sanity
check that the geometry actually has the promised distortion.

.. GENERATED FROM PYTHON SOURCE LINES 56-70

.. code-block:: Python


    m = problem.build_model()
    plotter = pv.Plotter(off_screen=True)
    plotter.add_mesh(m.grid, show_edges=True, opacity=0.7, color="#b8cde3")
    plotter.add_points(
        np.asarray(m.grid.points),
        render_points_as_spheres=True,
        point_size=12,
        color="red",
    )
    plotter.view_isometric()
    plotter.camera.zoom(1.1)
    plotter.show()




.. image-sg:: /gallery/verification/images/sphx_glr_example_verify_patch_test_001.png
   :alt: example verify patch test
   :srcset: /gallery/verification/images/sphx_glr_example_verify_patch_test_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 71-76

Acceptance
----------
The 1e-9 tolerance is conservative — we measure ~1e-19 on
this build.  A regression above 1e-12 would indicate a
precision-dropping change in the assembly / solve pipeline.

.. GENERATED FROM PYTHON SOURCE LINES 76-78

.. code-block:: Python


    assert r.passed, f"patch test failed: {r.computed:.3e} > {pv_.tolerance:.1e}"








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

   **Total running time of the script:** (0 minutes 0.221 seconds)


.. _sphx_glr_download_gallery_verification_example_verify_patch_test.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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