.. _ch:meshes:

Unstructured Meshes
===================

Coordinate Nested Dissection
----------------------------

Coordinate Nested Dissection (CND) (also referred to as Recursive Coordinate Bisection) is a recursive bisection scheme
that attempts to minimize the boundary between the subdomains (and therefore, the inter-processor communications) by
splitting the mesh in half normal to its longest dimension.

The algorithm:

#. Compute and project the center-of-mass for all meshes along the longest axis
#. Split this ordered list half to produce the bisection
#. Jump to 1. and repeat for all created meshes

.. image:: /images/cnd_mesh.png
  :alt: cnd_mesh
  :width: 400
  :align: center

.. centered:: Fig 10.1.1 Mesh

.. admonition:: Task

    Part the mesh from Fig. 10.1.1 in 8 partitions using CND and color the partitions with different colors.

GMSH
----

GMSH is a library to handle meshes. This includes among others creating meshes, read and write mesh files and partitioning meshes.
There are implementations for C++, Python and Julia.

.. admonition:: Task

    #. Use the language of your choice. Documentation under `GMSH Documentation <https://gmsh.info/dev/doc/texinfo/gmsh.pdf>`_
    #. Download the file `mesh <https://cloud.uni-jena.de/s/r7aqHnyXWneJAFT>`_
    #. Load the file with GMSH and partition the mesh using the following parameters:
        +------------------------------+----------+
        | Parameter                    | Value    |
        +==============================+==========+
        | Mesh partitioner             |0         |
        +------------------------------+----------+
        | Number of partitions         |10        |
        +------------------------------+----------+
        | Create partition topology    |1         |
        +------------------------------+----------+
        | Create ghost cells           |0         |
        +------------------------------+----------+
        | Create new physical groups   |0         |
        +------------------------------+----------+
        | Write file to disk           |0         |
        +------------------------------+----------+
        | Write one file per partition |0         |
        +------------------------------+----------+
    #. Show the mesh on your screen and take a screenshot of the partitioned mesh
    #. Submit the screenshot and your code