.. _R5.01.01:

**r5.01.01** Modal solvers and generalized problem solving (GEP)
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**Summary**

Whether to study the vibrations of a structure or to search for its buckling modes, the mechanic must often solve a modal problem: either generalized (GEP) or quadratic (QEP) () [R5.01.02]. To do this, **Code_Aster offers several methods** **via the operators** **CALC_MODES:** inverse powers and Rayleigh, Lanczos, IRA,,, Bathe & Wilson and QZ coefficients. They each have their scope of use, their advantages, their disadvantages and their development history.

**To deal effectively with large modal problems** (in terms of mesh size and/or number of modes sought), it is recommended to use the macro-command **CALC_MODES** with the option 'BANDE' divided into several sub-bands. It breaks down the modal calculation of a standard GEP (symmetric and real), into a succession of independent, less expensive, more robust and more accurate sub-calculations. Just sequentially, the **gains can be noteable**: factors 2 to 5 in time, 2 or 3 in peak RAM and 10 to 104 on the average error of the modes.

In addition, its **multi-level parallelism can provide additional gains** of the order of 20 in time and 2 in peak RAM, by reserving around sixty processors.

In the first part of the document, we summarize the general problem of solving a modal problem, the different classes of methods and their variations in public domain libraries. All things you need to have in mind before discussing, in the second part, the general architecture of a modal calculation in *Code_Aster*. Then we detail the numerical, computer and functional aspects of each of the approaches available in the code.

A specific chapter details the implementation of parallelism and intensive computing in the context of standard GEP modal calculations.




.. toctree::
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    self

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

    Introduction
    G_n_ralit_s_sur_les_solveurs_modaux_en_m_canique_des_structures
    Contexte
    M_thode_des_puissances_inverses__CALC_MODES_avec_OPTION_parmi___PROCHE___AJUSTE___SEPARE___
    M_thode_de_sous-espace__CALC_MODES_avec_OPTION_parmi___BANDE___CENTRE___PLUS_____
    M_thode_de_Lanczos__SOLVEUR_MODAL___F_METHODE__TRI_DIAG___
    Algorithme_IRA_SOLVEUR_MODAL__F__METHODE__SORENSEN___
    M_thode_de_Bathe_et_Wilson__SOLVEUR_MODAL___F_METHODE__JACOBI___
    M_thode_globale_QZ__SOLVEUR_MODAL___F_METHODE__QZ___
    Parall_lisme_et_calcul_intensif
    Bibliographie
    Description_des_versions_du_document
    Annexe_1__G_n_ralit_s_sur_l_algorithme_QR
    Annexe_2__Orthogonalisation_de_Gram-Schmidt
    Annexe_3__M_thode_de_Jacobi