G modeling
==============


Characteristics of G modeling
-------------------------------------

The seventh cut that we are testing does not correspond to a degenerate case, it is a case of cut in its own right which however has the particularity of presenting an edge where the *lsn* is cancelled exactly twice, at one of its ends and at its midpoint. An example of this configuration is shown in Figure.


.. image:: images/1000000000000250000002FC13DB62C5B4640774.jpg
    :width: 3.8799in
    :height: 4.5736in


.. _RefImage_1000000000000250000002FC13DB62C5B4640774.jpg:

**Figure** 8.1-a **: representation of the G modeling cuta**

The tetrahedron cut above is described in [:ref:`R7.02.12 <R7.02.12>`]. On either side of the *lsn* =0 surface there is a pyramid and a pentahedron. This tetrahedron will then give birth to 5 child sub-tetrahedra.


Characteristics of the mesh
----------------------------

To "find yourself" in this cutting configuration, *lsn* is defined node by node. Indeed, it is difficult for the*lsn* to show a function that brings us back to the configuration of Figure. The*lsn* value for each node is summarized in Figure.


.. image:: images/10000000000002AE000002FBF2D6612434759AB7.jpg
    :width: 4.1272in
    :height: 4.272in


.. _RefImage_10000000000002AE000002FBF2D6612434759AB7.jpg:

**Figure** 8.2-a **: value of the** *lsn* **in each node for G modeling**

The edges of TETRA are then intersected by the *level set* at the following 4 points:


.. csv-table::

    "Intersection point", "Coordinates"
    "IP1 ", "(0,0.1)"
    "IP2 ", "(0.5,0,0.5)"
    "IP3 ", "(0.7,0.3,0)"
    "IP4 ", "(0,0.3,0)"



Tested sizes and results
------------------------------

After executing command MODI_MODELE_XFEM, we check that the 4 intersection points IP1, IP2, IP3 and IP4 are in group NFISSU and that their position is correct.


.. csv-table::

    "Quantities tested", "Reference type", "Reference value", "Tolerance"
    "COORX IP1 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP1 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP1 ", "'ANALYTIQUE'", "1.0", "10E-06"
    "COORX IP2 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORY IP2 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP2 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORX IP3 ", "'ANALYTIQUE'", "0.7", "10E-06"
    "COORY IP3 ", "'ANALYTIQUE'", "0.3", "10E-06"
    "COORZ IP3 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORX IP4 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP4 ", "'ANALYTIQUE'", "0.3", "10E-06"
    "COORZ IP4 ", "'ANALYTIQUE'", "0.0", "10E-06"


The cut mesh (Figure) was also post-processed using SALOME. The cut obtained is in accordance with expectations, with 5 subtetrahedra that are consistent with the discontinuity.

.. image:: images/10000000000002B80000036AFF7C03228C811FC7.png
    :width: 4.5228in
    :height: 4.3217in


.. _RefImage_10000000000002B80000036AFF7C03228C811FC7.png:


.. image:: images/1000000000000364000002EA7AB10A7688B3FA44.png
    :width: 4.522in
    :height: 3.8083in


.. _RefImage_1000000000000364000002EA7AB10A7688B3FA44.png:

**Figure** 8.3-a **: G modeling cutting configuration**