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


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

3D modeling is used.


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

The 3D mesh contains 100 elements of type HEXA8 of dimension :math:`0.4\mathrm{\times }0.4\mathrm{\times }0.2\mathit{mm}`:


.. image:: images/1000020100000346000002D995CCAE0A41CACB38.png
    :width: 2.911in
    :height: 2.5898in


.. _RefImage_1000020100000346000002D995CCAE0A41CACB38.png:

Figure 3.2-1: mesh used

For the auxiliary grid, a 3D mesh containing 400 elements of type HEXA8 of dimension :math:`0.2\mathrm{\times }0.2\mathrm{\times }0.1\mathit{mm}` is used:


.. image:: images/100002010000033C000002CE4AD5B5F48318DF91.png
    :width: 3.0472in
    :height: 2.6417in


.. _RefImage_100002010000033C000002CE4AD5B5F48318DF91.png:

Figure 3.2-2: Auxiliary grid


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

After the two imposed propagations, we calculate the values of the level sets at the points of intersection between the segment connecting the end points of the background :math:`(\mathrm{0,2}.189\mathrm{,0}.156)` and :math:`(\mathrm{4,2}.189\mathrm{,0}.156)` (see § :ref:`2.2 <RefNumPara__32466127>`) and the faces of the elements of the mesh and we will check that the maximum and minimum values obtained are equal to zero. Assuming that the mesh is coarse, a tolerance equal to 15% of the length of the smallest edge of the mesh is used, i.e. :math:`0.15\mathrm{\cdot }0.2\mathit{mm}\mathrm{=}0.03\mathit{mm}`. So we accept the value of the level set at the bottom point in question if and only if it is in the interval :math:`\mathrm{[}\mathrm{-}0.03\mathrm{,0}.03\mathrm{]}`.