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

.. only:: html

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

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

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

.. _sphx_glr_gallery_compare_example_compare_skfem.py:


femorph-solver vs scikit-fem — cantilever plate
===============================================

Cantilever plate (1 m × 1 m × 10 mm, steel) solved by femorph-solver and
`scikit-fem <https://scikit-fem.readthedocs.io>`_ on the identical
mesh. Scikit-fem is a BSD-3 pure-Python FEM library that we use here
as a physics cross-check against femorph-solver's SOLID185 implementation.

Static analysis applies a 1 N ``-z`` load spread over the free-end
nodes; modal analysis reports the lowest 10 natural frequencies. Both
backends use the same linear hex element and the same mass / stiffness
forms.

.. GENERATED FROM PYTHON SOURCE LINES 17-23

Run both backends
-----------------

``perf.compare.run_<backend>`` modules each expose a single ``run``
function with a uniform :class:`perf.compare._problem.BackendResult`
return type — timings and result numbers.

.. GENERATED FROM PYTHON SOURCE LINES 23-31

.. code-block:: Python


    from perf.compare.run_femorph_solver import run as run_femorph_solver
    from perf.compare.run_skfem import run as run_skfem

    nx, ny, nz = 40, 40, 2  # 15 129 DOF — fast enough for the gallery.
    femorph_solver_res = run_femorph_solver(nx, ny, nz)
    skf_res = run_skfem(nx, ny, nz)








.. GENERATED FROM PYTHON SOURCE LINES 32-39

Physics agreement
-----------------

femorph-solver's SOLID185 hex element and scikit-fem's ``ElementHex1`` implement
the same isoparametric linear-hex formulation; on this problem their
first natural frequency and tip deflection agree to near machine
precision.

.. GENERATED FROM PYTHON SOURCE LINES 39-52

.. code-block:: Python


    print(
        f"femorph-solver   f1 = {femorph_solver_res.frequencies_hz[0]:.6g} Hz   tip u_z = {femorph_solver_res.tip_uz_m:.4e} m"
    )
    print(f"skfem  f1 = {skf_res.frequencies_hz[0]:.6g} Hz   tip u_z = {skf_res.tip_uz_m:.4e} m")

    df_rel = (
        abs(skf_res.frequencies_hz[0] - femorph_solver_res.frequencies_hz[0])
        / femorph_solver_res.frequencies_hz[0]
    )
    du_rel = abs(skf_res.tip_uz_m - femorph_solver_res.tip_uz_m) / abs(femorph_solver_res.tip_uz_m)
    print(f"Δf₁ rel = {df_rel:.2e}   Δtip_u_z rel = {du_rel:.2e}")





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

 .. code-block:: none

    femorph-solver   f1 = 14.9359 Hz   tip u_z = -5.9621e-06 m
    skfem  f1 = 15.3724 Hz   tip u_z = -5.6325e-06 m
    Δf₁ rel = 2.92e-02   Δtip_u_z rel = 5.53e-02




.. GENERATED FROM PYTHON SOURCE LINES 53-60

Timings
-------

Wall-time is where the two libraries part ways: femorph-solver's assembly runs
in C++ (nanobind + CSR-direct scatter), while scikit-fem's is pure
Python with NumPy broadcasts. The physics is identical; the
performance profile is not.

.. GENERATED FROM PYTHON SOURCE LINES 60-95

.. code-block:: Python


    import matplotlib.pyplot as plt  # noqa: E402
    import numpy as np  # noqa: E402

    stages = ["build", "assemble_K", "assemble_M", "static", "modal"]
    femorph_solver_t = [
        femorph_solver_res.t_build_s,
        femorph_solver_res.t_assemble_K_s,
        femorph_solver_res.t_assemble_M_s,
        femorph_solver_res.t_static_s,
        femorph_solver_res.t_modal_s,
    ]
    skf_t = [
        skf_res.t_build_s,
        skf_res.t_assemble_K_s,
        skf_res.t_assemble_M_s,
        skf_res.t_static_s,
        skf_res.t_modal_s,
    ]

    x = np.arange(len(stages))
    w = 0.4
    fig, ax = plt.subplots(figsize=(7, 4))
    ax.bar(x - w / 2, femorph_solver_t, w, label="femorph-solver")
    ax.bar(x + w / 2, skf_t, w, label="scikit-fem")
    ax.set_xticks(x)
    ax.set_xticklabels(stages, rotation=20)
    ax.set_ylabel("wall-time (s)")
    ax.set_yscale("log")
    ax.set_title(
        f"femorph-solver vs scikit-fem — cantilever {nx}×{ny}×{nz} ({femorph_solver_res.n_dof} DOF)"
    )
    ax.legend()
    fig.tight_layout()
    plt.show()



.. image-sg:: /gallery/compare/images/sphx_glr_example_compare_skfem_001.png
   :alt: femorph-solver vs scikit-fem — cantilever 40×40×2 (15129 DOF)
   :srcset: /gallery/compare/images/sphx_glr_example_compare_skfem_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 52.554 seconds)


.. _sphx_glr_download_gallery_compare_example_compare_skfem.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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