.. _R6.02.03:

**r6.02.03** Overview of direct linear solvers and the use of MUMPS
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**Summary**

In the context of thermo-mechanical simulations with *Code_Aster*, **most of the calculation costs often come from the construction and resolution of linear systems**. To perform these resolutions more effectively, **Code_Astera has chosen to integrate the direct method deployed in package MUMPS** ('Multifrontal Massively Parallel sparse direct Solver; P.R.Amestoy, J.Y.L'Excellent et al; CERFACS/CNRS/L'Excellent et al;//L'Excellent et al;//ENS Lyon IRIT/INRIA /University of Bordeaux). This is in addition to its "homemade" multifrontend (C.Rose) and its other solvers: 'LDLT', 'GCPC' and 'PETSC'.

In distributed parallel mode and in Out-Of-Core, the *Aster* + MUMPS coupling provides **gains in CPU of the order of the dozen** on 32 processors. And this, for **consumption RAM** **, a**behavior/functional scope**and a**precision of the results**at least as good as**those of the native multifronter** of the code.

On big problems, by activating BLR compressions, you can even gain an additional factor of two or three. This product, *via* the parallelism it exhibits and its advanced functionalities (pivoting, pre/post-processing, quality of the solution...) greatly facilitates the passage of standard studies. Moreover, it often remains the **only viable alternative** to exploit certain modellations/analyses (almost incompressible, X- FEM...) or to go from very large studies (as a precise direct solver or as a preconditioner, cf. option 'LDLT_SP' of 'GCPC'/'PETSC').

**In the first part of the document** we summarize the general problem of solving linear systems, then we discuss the main families of sparse direct solvers and their variations in public domain libraries.

Everything you need to have in mind before addressing, **in the second part**, the MUMPS package through its main characteristics and advanced functionalities. Then we detail the numerical, computer and functional aspects of its integration into *Code_Aster*. Finally, we conclude with some numerical results.

**For more details and advice** on the use of linear solvers, you can consult the specific instructions for use [:external:ref:`U4.50.01 <U4.50.01>`]/[U2.08.03]. The related problems of improving the performance (RAM/CPU) of a calculation and, of the use of parallelism, are also the subject of detailed instructions: [:external:ref:`U1.03.03 <U1.03.03>`] and [:external:ref:`U2.08.06 <U2.08.06>`].




.. toctree::
    :hidden:

    self

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

    G_n_ralit_s_sur_les_solveurs_directs
    Le_package_MUMPS
    Implantation_dans_Code_Aster
    Conclusion
    Bibliographie
    Historique_des_versions_du_document
    Annexe_n_1__Principe_des_compressions_BLR_dans_MUMPS