.. _R3.06.07:

**r3.06.07** Diagonalization of the thermal mass matrix
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**Summary:**

To improve the consistency of the solution in transient thermal problems, one of the solutions consists in "lumping" (i.e.: condensing on the diagonal) the thermal mass matrix (capacity matrix).

This possibility is accessible by the models PLAN_DIAG, AXIS_DIAG and 3D_ DIAG for the phenomenon THERMIQUE. It is activated when the thermal calculation commands THER_LINEAIRE and THER_NON_LINE are called.

When using these models, only linear finite elements (2D and 3D) have a lumped mass matrix. In fact, direct diagonalization does not give satisfactory results for quadratic finite elements, so it is not allowed.

The theoretical results are illustrated by the thermo-mechanical calculation of a cylinder subjected to thermal shock.




.. toctree::
    :hidden:

    self

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

    Introduction
    Principe_du_maximum
    M_thode_de_diagonalisation_retenue_et_types_d__l_ments
    Mise_en__uvre_dans_Code_Aster
    Calcul_thermique_d_un_cylindre_soumis___un_choc_froid
    Conclusion
    Bibliographie
    Description_des_versions_du_document