*********************
GooseFEM::Mesh::Quad4
*********************

.. note::

  Source:

  .. code-block:: cpp

    #include <GooseFEM/MeshQuad4.h>

``GooseFEM::Mesh::Quad4::Regular``
==================================

.. code-block:: cpp

  GooseFEM::Mesh::Quad4::Regular(size_t nx, size_t ny, double h=1.);

Regular mesh of linear quadrilaterals in two-dimensions. The element edges are all of the same size :math:`h` (by default equal to one), optional scaling can be applied afterwards. For example the mesh shown below that consists of 21 x 11 elements. In that image the element numbers are indicated with a color, and likewise for the boundary nodes.

.. image:: figures/MeshQuad4/Regular/example.svg
  :width: 500px
  :align: center

Methods:

.. code-block:: cpp

  // A matrix with on each row a nodal coordinate:
  // [ x , y ]
  MatD = GooseFEM::Mesh::Quad4::Regular.coor();

  // A matrix with the connectivity, with on each row to the nodes of each element
  MatS = GooseFEM::Mesh::Quad4::Regular.conn();

  // A list of boundary nodes
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesBottom();
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesTop();
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesLeft();
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesRight();

  // A matrix with periodic node pairs on each row:
  // [ independent nodes, dependent nodes ]
  MatS = GooseFEM::Mesh::Quad4::Regular.nodesPeriodic();

  // The node at the origin
  size_t = GooseFEM::Mesh::Quad4::Regular.nodeOrigin();

  // A matrix with DOF-numbers: two per node in sequential order
  MatS = GooseFEM::Mesh::Quad4::Regular.dofs();

  // A matrix with DOF-numbers: two per node in sequential order
  // All the periodic repetitions are eliminated from the system
  MatS = GooseFEM::Mesh::Quad4::Regular.dofsPeriodic();

``GooseFEM::Mesh::Quad4::FineLayer``
====================================

Regular mesh with a fine layer of quadrilateral elements, and coarser elements above and below.

.. image:: figures/MeshQuad4/FineLayer/example.svg
  :width: 500px
  :align: center

.. note::

  The coarsening depends strongly on the desired number of elements in horizontal elements. The becomes clear from the following example:

  .. code-block:: cpp

    mesh = GooseFEM::Mesh::Quad4::FineLayer(6*9  ,51); // left   image :  546 elements
    mesh = GooseFEM::Mesh::Quad4::FineLayer(6*9+3,51); // middle image :  703 elements
    mesh = GooseFEM::Mesh::Quad4::FineLayer(6*9+1,51); // right  image : 2915 elements

  .. image:: figures/MeshQuad4/FineLayer/behavior.svg
    :width: 1000px
    :align: center

Methods:

.. code-block:: cpp

  // A matrix with on each row a nodal coordinate:
  // [ x , y ]
  MatD = GooseFEM::Mesh::Quad4::Regular.coor();

  // A matrix with the connectivity, with on each row to the nodes of each element
  MatS = GooseFEM::Mesh::Quad4::Regular.conn();

  // A list of boundary nodes
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesBottom();
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesTop();
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesLeft();
  ColS = GooseFEM::Mesh::Quad4::Regular.nodesRight();

  // A matrix with periodic node pairs on each row:
  // [ independent nodes, dependent nodes ]
  MatS = GooseFEM::Mesh::Quad4::Regular.nodesPeriodic();

  // The node at the origin
  size_t = GooseFEM::Mesh::Quad4::Regular.nodeOrigin();

  // A matrix with DOF-numbers: two per node in sequential order
  MatS = GooseFEM::Mesh::Quad4::Regular.dofs();

  // A matrix with DOF-numbers: two per node in sequential order
  // All the periodic repetitions are eliminated from the system
  MatS = GooseFEM::Mesh::Quad4::Regular.dofsPeriodic();

  // A list with the element numbers of the fine elements in the center of the mesh
  // (highlighted in the plot below)
  ColS = GooseFEM::Mesh::Quad4::FineLayer.elementsFine();

    .. image:: figures/MeshQuad4/FineLayer/example_elementsFine.svg
      :width: 500px
      :align: center