FElupe documentation
====================

FElupe is a Python 3.10+ finite element analysis package focusing on the formulation and numerical solution of nonlinear problems in continuum mechanics of solid bodies. This package is intended for scientific research, but is also suitable for running nonlinear simulations in general. In addition to the transformation of general weak forms into sparse vectors and matrices, FElupe provides an efficient high-level abstraction layer for the simulation of the deformation of solid bodies.

.. grid::

   .. grid-item-card:: 🏃 Beginner's Guide
      :link: tutorials
      :link-type: ref

      New to FElupe? The Beginner's Guide contains an introduction to the concept of FElupe.

   .. grid-item-card:: 📖 API reference
      :link: felupe-api
      :link-type: ref

      The reference guide contains a detailed description of the FElupe API. It describes how the methods work and which parameters can be used. Requires an understanding of the key concepts.

.. grid::

   .. grid-item-card:: ☎ How-To
      :link: how-to
      :link-type: ref

      Step-by-step guides for specific tasks or problems with a focus on practical usability instead of completeness. Requires an understanding of the key concepts.

   .. grid-item-card:: 📚 Examples
      :link: examples
      :link-type: ref

      A gallery of examples.


.. admonition:: Highlights
   :class: admonition

   + 100% Python package built with `NumPy <https://numpy.org/>`_ and `SciPy <https://scipy.org/>`_

   + easy to learn and productive high-level :ref:`API <felupe-api>`

   + nonlinear deformation of :class:`solid bodies <felupe.SolidBody>`

   + interactive views on meshes, fields and solid bodies (using `PyVista <https://pyvista.org/>`_)

   + typical :ref:`finite elements <felupe-api-element>`

   + cartesian, axisymmetric, plane strain and mixed fields

   + :ref:`hyperelastic material models <felupe-api-constitution-autodiff>` with :class:`automatic differentiation <felupe.Hyperelastic>`


Installation
------------
Install Python, open a terminal and run

.. image:: https://img.shields.io/pypi/v/felupe.svg
   :target: https://pypi.python.org/pypi/felupe/

.. code-block:: shell

   pip install felupe[all]

where ``[all]`` is a combination of ``[autodiff,io,parallel,plot,progress,view]`` and installs all optional dependencies. FElupe has minimal requirements, all available at PyPI supporting all platforms.

* `numpy <https://github.com/numpy/numpy>`_ for array operations
* `scipy <https://github.com/scipy/scipy>`_ for sparse matrices

In order to make use of all features of FElupe, it is suggested to install all optional dependencies.

* `einsumt <https://github.com/mrkwjc/einsumt>`_ for parallel (threaded) assembly
* `jax <https://github.com/jax-ml/jax>`_ for automatic differentiation in material formulations (JAX-based)
* `h5py <https://github.com/h5py/h5py>`_ for writing XDMF result files
* `matplotlib <https://github.com/matplotlib/matplotlib>`_ for plotting graphs
* `meshio <https://github.com/nschloe/meshio>`_ for mesh-related I/O
* `pyvista <https://github.com/pyvista/pyvista>`_ for interactive visualizations
* `tensortrax <https://github.com/adtzlr/tensortrax>`_ for automatic differentiation in material formulations (NumPy-based)
* `tqdm <https://github.com/tqdm/tqdm>`_ for showing progress bars during job evaluations

The development version may contain not yet released bug fixes and features. Consider using the ``--user`` option to install the package into your home directory (see `pip documentation <https://pip.pypa.io/en/stable/user_guide/#user-installs>`_ for more details). To install FElupe from the latest development branch, use

.. code-block:: shell

   pip install git+https://github.com/adtzlr/felupe.git@main

or clone the repository and install the package in editable mode.

.. code-block:: shell

   git clone https://github.com/adtzlr/felupe.git
   cd felupe
   pip install --editable .

Optional dependencies may also be installed by replacing the last line.

.. code-block:: shell

   pip install --editable ".[all]"

Extension Packages
------------------

The capabilities of FElupe may be enhanced with extension packages created by the community.

+-----------------------------------------------------------+------------------------------------------------------------+
| Package                                                   | Description                                                |
+===========================================================+============================================================+
| `contique <https://github.com/adtzlr/contique>`_          | Numerical continuation of nonlinear equilibrium equations. |
+-----------------------------------------------------------+------------------------------------------------------------+
| `hyperelastic <https://github.com/adtzlr/hyperelastic>`_  | Constitutive hyperelastic material formulations            |
+-----------------------------------------------------------+------------------------------------------------------------+
| `matadi <https://github.com/adtzlr/matadi>`_              | Material Definition with Automatic Differentiation (AD)    |
+-----------------------------------------------------------+------------------------------------------------------------+
| `statescale <https://github.com/adtzlr/statescale>`_      | Snapshot-Driven State Upscaling                            |
+-----------------------------------------------------------+------------------------------------------------------------+
| `tensortrax <https://github.com/adtzlr/tensortrax>`_      | Differentiable Tensors based on NumPy Arrays               |
|                                                           | (bundled with FElupe)                                      |
+-----------------------------------------------------------+------------------------------------------------------------+
| `feplot <https://github.com/ZAARAOUI999/feplot>`_         | A visualization tool for FElupe                            |
+-----------------------------------------------------------+------------------------------------------------------------+

Performance
-----------
This is a simple benchmark to compare assembly times for linear elasticity and hyperelasticity on tetrahedrons.

.. tab:: Assembly Runtimes

   .. image:: _static/benchmark.png
      :width: 400px

   +----------------+-------------------+
   | Analysis       |        DOF/s      |
   +================+===================+
   | Linear-Elastic |  130039 +/-23464  |
   +----------------+-------------------+
   | Hyperelastic   |  116819 +/-21979  |
   +----------------+-------------------+

   Tested on: Windows 10, Python 3.11, Intel® Core™ i7-11850H @ 2.50GHz, 32GB RAM.


.. tab:: Source Code

   .. code-block:: python

      from timeit import timeit

      import matplotlib.pyplot as plt
      import numpy as np

      import felupe as fem


      def pre_linear_elastic(n, **kwargs):
          mesh = fem.Cube(n=n).triangulate()
          region = fem.RegionTetra(mesh)
          field = fem.FieldContainer([fem.Field(region, dim=3)])
          umat = fem.LinearElastic(E=1, nu=0.3)
          solid = fem.SolidBody(umat, field)
          return mesh, solid


      def pre_hyperelastic(n, **kwargs):
          mesh = fem.Cube(n=n).triangulate()
          region = fem.RegionTetra(mesh)
          field = fem.FieldContainer([fem.Field(region, dim=3)])
          umat = fem.NeoHookeCompressible(mu=1.0, lmbda=2.0)
          solid = fem.SolidBody(umat, field)
          return mesh, solid


      print("# Assembly Runtimes")
      print("")
      print("|   DOF   | Linear-Elastic in s | Hyperelastic in s |")
      print("| ------- | ------------------- | ----------------- |")

      points_per_axis = np.round((np.logspace(3, 5, 6) / 3)**(1 / 3)).astype(int)

      number = 3
      parallel = False

      runtimes = np.zeros((len(points_per_axis), 2))

      for i, n in enumerate(points_per_axis):
          mesh, solid = pre_linear_elastic(n)
          matrix = solid.assemble.matrix(parallel=parallel)
          time_linear_elastic = (
              timeit(lambda: solid.assemble.matrix(parallel=parallel), number=number) / number
          )

          mesh, solid = pre_hyperelastic(n)
          matrix = solid.assemble.matrix(parallel=parallel)
          time_hyperelastic = (
              timeit(lambda: solid.assemble.matrix(parallel=parallel), number=number) / number
          )

          runtimes[i] = time_linear_elastic, time_hyperelastic

          print(
              f"| {mesh.points.size:7d} | {runtimes[i][0]:19.2f} | {runtimes[i][1]:17.2f} |"
          )

      dofs_le = points_per_axis ** 3 * 3 / runtimes[:, 0]
      dofs_he = points_per_axis ** 3 * 3 / runtimes[:, 1]

      print("")
      print("| Analysis       |        DOF/s      |")
      print("| -------------- | ----------------- |")
      print(
          f"| Linear-Elastic |   {np.mean(dofs_le):5.0f} +/-{np.std(dofs_le):5.0f}  |"
      )
      print(f"| Hyperelastic   |   {np.mean(dofs_he):5.0f} +/-{np.std(dofs_he):5.0f}  |")

      plt.figure()
      plt.loglog(
          points_per_axis ** 3 * 3,
          runtimes[:, 1],
          "C0",
          label=r"Stiffness Matrix (Hyperelastic)",
      )
      plt.loglog(
          points_per_axis ** 3 * 3,
          runtimes[:, 0],
          "C1--",
          label=r"Stiffness Matrix (Linear-Elastic)",
      )
      plt.xlabel(r"Number of degrees of freedom $\longrightarrow$")
      plt.ylabel(r"Runtime in s $\longrightarrow$")
      plt.legend()
      plt.tight_layout()
      plt.savefig("benchmark.png")


.. toctree::
   :maxdepth: 1
   :caption: Contents:
   
   tutorial/index
   examples/index
   howto
   felupe

License
-------

FElupe - Finite Element Analysis (C) 2021-2026 Andreas Dutzler, Graz (Austria).

This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program. If not, see `<https://www.gnu.org/licenses/>`_.

Indices and tables
==================

* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`