D modeling
==============


Characteristics of modeling D
-------------------------------------

The fourth cut we are testing again corresponds to a case where two of the edges of TETRA10 see the *lsn* cancel out exactly twice, at one of their ends and at their midpoint. An example of this configuration is shown in Figure.


.. image:: images/100000000000026A0000030B3542E5A76E6E450A.jpg
    :width: 4.0362in
    :height: 4.6146in


.. _RefImage_100000000000026A0000030B3542E5A76E6E450A.jpg:

**Figure** 5.1-a **: representation of the cut of the D 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/1000000000000233000002E9719E74C2E5575DEE.jpg
    :width: 3.7244in
    :height: 4.7193in


.. _RefImage_1000000000000233000002E9719E74C2E5575DEE.jpg:

**Figure** 5.1-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/10000000000002AD00000302CDF29812CFCCEA3C.jpg
    :width: 3.9181in
    :height: 4.3547in


.. _RefImage_10000000000002AD00000302CDF29812CFCCEA3C.jpg:

**Figure** 5.2-a **: value of the** *lsn* **in each node for D modelling**

The edges of TETRA are then intersected by the *level set* at the following 5 points:


.. csv-table::

    "Intersection point", "Coordinates"
    "IP1 ", "(1,0,0)"
    "IP2 ", "(0.5,0.5,0)"
    "IP3 ", "(0.5,0,0.5)"
    "IP4 ", "(0,0.25,0.75)"
    "IP5 ", "(0,0, :math:`\frac{6}{7}`)"



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

After executing command MODI_MODELE_XFEM, we check that the 5 intersection points IP1, IP2,, IP3, IP4 and IP5 are in the group NFISSU and that their position is correct.


.. csv-table::

    "Quantities tested", "Reference type", "Reference value", "Tolerance"
    "COORX IP1 ", "'ANALYTIQUE'", "1.0", "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'", "0.5", "10E-06"
    "COORZ IP2 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORX IP3 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORY IP3 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP3 ", "'ANALYTIQUE'", "0.5", "10E-06"
    "COORX IP4 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP4 ", "'ANALYTIQUE'", "0.25", "10E-06"
    "COORZ IP4 ", "'ANALYTIQUE'", "0.75", "10E-06"
    "COORX IP5 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORY IP5 ", "'ANALYTIQUE'", "0.0", "10E-06"
    "COORZ IP5 ", "'ANALYTIQUE'", "0.857142857", "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/1000000000000210000002DEC4EA546D4D6ABC34.png
    :width: 4.2063in
    :height: 4.861in


.. _RefImage_1000000000000210000002DEC4EA546D4D6ABC34.png:


.. image:: images/10000000000003410000031DB5D4204669ACBA99.png
    :width: 4.2063in
    :height: 3.3862in


.. _RefImage_10000000000003410000031DB5D4204669ACBA99.png:

**Figure** 5.3-a **: D modeling cutting configuration**