Modeling A
==============


Characteristics of modeling A
-------------------------------------

The first cut we're testing corresponds to the case where one of the edges of TETRA10 sees 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/10000000000002570000030F84E075CC2711C6B5.jpg
    :width: 3.9972in
    :height: 4.4071in


.. _RefImage_10000000000002570000030F84E075CC2711C6B5.jpg:

**Figure** 2.1-a **: representation of the cut of modeling A**

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


.. image:: images/10000000000001AB00000236EAF323F2C827B234.jpg
    :width: 2.7583in
    :height: 3.178in


.. _RefImage_10000000000001AB00000236EAF323F2C827B234.jpg:

**Figure** 2.1-b **: :** **corresponding healthy configuration**


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

To "find yourself" in this cutting configuration, the *lsn* is chosen spherical, with a center C (:math:`\frac{3}{4}`, :math:`\frac{3}{4}`, :math:`\frac{1}{4}`) and with a radius :math:`R=\frac{\sqrt{(19)}}{4}`

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


.. csv-table::

    "Intersection point", "Coordinates"
    "IP1 ", "(0,0,0)"
    "IP2 ", "(0,0,0.5)"
    "IP3 ", "(:math:`\frac{3-\sqrt{(5)}}{4}` ,0, :math:`\frac{\sqrt{(5)}+1}{4}`)"
    "IP4 ", "(0, :math:`\frac{3-\sqrt{(5)}}{4}`, :math:`\frac{\sqrt{(5)}+1}{4}`)"



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'", "0.0", "10E-06"
    "COORX IP2 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP2 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP2 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORX IP3 ", "'ANALYTIQUE'", "0.19098300", "10E-06"
    "COORY IP3 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP3 ", "'ANALYTIQUE'", "0.80901699", "10E-06"
    "COORX IP4 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP4 ", "'ANALYTIQUE'", "0.19098300", "10E-06"
    "COORZ IP4 ", "'ANALYTIQUE'", "0.80901699", "10E-06"


The cut mesh (Figure) was also post-processed using SALOME. The cut obtained is in accordance with expectations, with 4 subtetrahedra that are consistent with the discontinuity.


.. image:: images/1000020100000268000001C49E429EE9C384782B.png
    :width: 4.5264in
    :height: 4.0283in


.. _RefImage_1000020100000268000001C49E429EE9C384782B.png:


.. image:: images/1000020100000242000001C5C17CE35AD98577A4.png
    :width: 4.5354in
    :height: 4.0898in


.. _RefImage_1000020100000242000001C5C17CE35AD98577A4.png:

**Figure** 2.3-a **: A modeling cutting configuration**