.. _V3.04.321:

.. image:: images/1000020100000212000002025363F35EC100A383.png
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    :height: 4.2118in


.. _RefImage_1000020100000212000002025363F35EC100A383.png:

Figure 1.1-1: Domain geometry and interface position


**v3.04.321** SSLV321 - Validation of XFEM preconditioning for a grazing interface
=========================================================================================

**Summary:**

This test validates the pre-conditioner dedicated to quadratic XFEM elements. The problem corresponds to that of a 3D block cut by an interface XFEM. Multiaxial compression is applied over the entire surface of the block, including on interface XFEM. The expected analytical solution is a :math:`{P}_{1}` move within the domain. This solution is captured naturally by the elements :math:`{P}_{1}` and :math:`{P}_{2}` of Code_Aster.

As the interface passes near the mesh nodes, the conditioning of the stiffness matrix increases [:ref:`1,2 <1,2>`]. The usual strategies, used in Code_Aster (readjusting the interface to the nodes and eliminating ddls Heaviside), based on "estimative" criteria, are not always adapted to control the conditioning and the precision of the results [:ref:`2 <2>`]. These disadvantages are all the more penalizing, with quadratic elements.

The new strategy (construction of a diagonal preconditioner by blocks) makes it possible to overcome all these disadvantages [:ref:`3 <3>`].

This test includes 5 models:


* :math:`A`: a HEXA8 :math:`\mathrm{3D}` modeling with an interface XFEM of equation :math:`x+y+z+0.01\mathrm{=}0`


* :math:`B`: a HEXA20 :math:`\mathrm{3D}` modeling with an interface XFEM of equation :math:`x+y+z+0.1=0`


* :math:`C`: a HEXA20 :math:`\mathrm{3D}` modeling with an interface XFEM of equation :math:`x+y+z+0.01\mathrm{=}0`


* :math:`D`: a HEXA8 :math:`\mathrm{3D}` modeling with an interface XFEM of equation :math:`x+y+z+0.011=0`


* :math:`E`: a HEXA8 :math:`\mathrm{3D}` modeling with an interface XFEM of equation :math:`x+y+z+0.011=0`


.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Probl_me_de_r_f_rence_en_3D
    Solution_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Mod_lisation_E
    Synth_se_des_r_sultats