F modeling
==============


Characteristics of F modeling
-------------------------------------

The sixth cut we are testing corresponds to a case where one of the edges of TETRA10 sees the *lsn* cancel out at its 3 nodes while two adjacent edges see the *lsn* cancel out exactly twice, at one of its ends and at its midpoint. An example of this configuration is shown in Figure.


.. image:: images/1000000000000285000002E780F1A5492D09B677.jpg
    :width: 3.9217in
    :height: 4.7035in


.. _RefImage_1000000000000285000002E780F1A5492D09B677.jpg:

**Figure** 7.1-a **: representation of the cut of the F** modeling

For cutting, we come back to the more classical case represented in Figure, whose subtetrahedron cutting is detailed in [:ref:`R7.02.12 <R7.02.12>`].


.. image:: images/100000000000024D000002E6F82599B79686396C.jpg
    :width: 3.9354in
    :height: 4.5402in


.. _RefImage_100000000000024D000002E6F82599B79686396C.jpg:

**Figure** 7.1-b **: :** **corresponding healthy configuration**


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/10000000000002A90000030C13562C860C2C5C1B.jpg
    :width: 3.9346in
    :height: 4.4799in


.. _RefImage_10000000000002A90000030C13562C860C2C5C1B.jpg:

**Figure** 7.2-a **: value of the** *lsn* **in each node for F** modeling

The edges of TETRA are then intersected by the *level set* at the following 6 points:


.. csv-table::

    "Intersection point", "Coordinates"
    "IP1 ", "(0,1,0)"
    "IP2 ", "(0,0.1)"
    "IP3 ", "(0,0.5,0.5)"
    "IP4 ", "(0,0.5,0)"
    "IP5 ", "(0.5,0,0.5)"
    "IP6 ", "(:math:`\frac{2}{3}` ,0,0)"



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

After executing command MODI_MODELE_XFEM, we check that the 6 intersection points IP1, IP2,, IP3,, IP4, IP5 and IP6 are in the 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'", "1.0", "10E-06"
    "COORZ IP1 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORX IP2 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP2 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP2 ", "'ANALYTIQUE'", "1.0", "10E-06"
    "COORX IP3 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP3 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORZ IP3 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORX IP4 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP4 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORZ IP4 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORX IP5 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORY IP5 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP5 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORZ IP6 ", "'ANALYTIQUE'", "0.66666666666", "10E-06"
    "COORZ IP6 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP6 ", "'ANALYTIQUE'", "0.0", "10E-06"


The cut mesh (Figure) was also post-processed using SALOME. The cut obtained is in accordance with expectations, with 6 subtetrahedra that are consistent with the discontinuity.

.. image:: images/100000000000022F000003214F4A34D09B00DFC4.png
    :width: 4.3528in
    :height: 4.6839in


.. _RefImage_100000000000022F000003214F4A34D09B00DFC4.png:


.. image:: images/1000000000000368000002CADF503392C2D2DEDC.png
    :width: 4.3543in
    :height: 3.5736in


.. _RefImage_1000000000000368000002CADF503392C2D2DEDC.png:

**Figure** 7.3-a **: F modeling cutting configuration**