Tutorial Page
===============


Optimization
-----------------

Below is a minimal working example that performs a topology optimization.
This will run a compliance minimization with OC method.

Optimizer Configuration, and Run
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: python

    import sktopt

    cfg = sktopt.core.optimizers.OC_Config(
        dst_path="./result/tutorial_box_oc",
        vol_frac=sktopt.tools.SchedulerConfig.constant(
            target_value=0.4
        ),
        max_iters=10,
        record_times=10,
        export_img=True
    )
    optimizer = sktopt.core.OC_Optimizer(cfg, mytask)
    optimizer.parameterize()
    optimizer.optimize()

But before running the optimization, we need to set up the task configuration and the design variables.

Task Definition
-----------------

Shape modeling and its basis function
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In this example, we use skfem.ElementHex1(), which represents a **first-order (linear) hexahedral element**.  
Scikit-Topt currently supports:

- 3D: Hexahedral P1 (`ElementHex1`)
- 3D Tetrahedral P1 (`ElementTetP1`)


.. code-block:: python

    import skfem
    import sktopt

    x_len = 8.0
    y_len = 8.0
    z_len = 1.0
    mesh_size = 0.2

    mesh = sktopt.mesh.toy_problem.create_box_hex(
        x_len, y_len, z_len, mesh_size
    )
    e = skfem.ElementVector(skfem.ElementHex1())
    basis = skfem.Basis(mesh, e, intorder=1)


Load Basis from Model File 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Scikit-Topt loads meshes via scikit-fem, which internally relies on meshio.
Therefore, the library supports all mesh formats that meshio supports:

Gmsh v2 (ASCII / binary)

Gmsh v4 (ASCII / binary)

When using .msh files, users may provide physical groups (surfaces/volumes)
which scikit-topt interprets as boundary and subdomain tags.


.. code-block:: python

    import skfem
    import sktopt

    mesh_path = "./data/model.msh"
    basis = sktopt.mesh.loader.basis_from_file(mesh_path, intorder=1)


Task Configuration
~~~~~~~~~~~~~~~~~~~~

.. code-block:: python

    dirichlet_in_range = sktopt.mesh.utils.get_points_in_range(
        (0.0, 0.05), (0.0, y_len), (0.0, z_len)
    )
    dirichlet_dir = "all"

    eps = mesh_size
    force_in_range_0 = sktopt.mesh.utils.get_points_in_range(
        (x_len, x_len), (y_len-eps, y_len), (0, z_len)
    )
    force_in_range_1 = sktopt.mesh.utils.get_points_in_range(
        (x_len, x_len), (0, eps), (0, z_len)
    )
    force_dir_type = ["u^2", "u^2"]
    force_value = [-100, 100]

    boundaries = {
        "dirichlet": dirichlet_in_range,
        "force_0": force_in_range_0,
        "force_1": force_in_range_1
    }
    mesh = mesh.with_boundaries(boundaries)
    subdomains = {"design": np.array(range(mesh.nelements))}
    mesh = mesh.with_subdomains(subdomains)

    e = skfem.ElementVector(skfem.ElementHex1())
    basis = skfem.Basis(mesh, e, intorder=2)
    E0 = 210e3
    mytask = task.LinearElasticity.from_mesh_tags(
        basis,
        "all",
        force_dir_type,
        force_value,
        E0,
        0.30,
    )


Results and Visualization
-----------------------------

The results of the optimization are stored in the directory specified by cfg.dst_path.
They include visualizations of the density distribution and graphs showing the evolution
of optimization quantities such as compliance, volume fraction, and sensitivities.

## Examples 

.. figure:: https://media.githubusercontent.com/media/kevin-tofu/scikit-topt/master/assets/ex-multi-load-condition.jpg
   :width: 400px
   :align: center

   Multi-load condition visualization.

.. figure:: https://media.githubusercontent.com/media/kevin-tofu/scikit-topt/master/assets/ex-multi-load-v-50.jpg
   :width: 400px
   :align: center

   Density distribution after optimization under multi-load conditions.

.. raw:: html

   <video width="640" height="360" controls>
     <source src="_static/animation-box-rho.mp4" type="video/mp4">
     Your browser does not support the video tag.
   </video>