.. _R6.01.02: **r6.01.02** Overview of the conjugate gradient: GCPC Aster and the use of PETSc ====================================================================================== **Summary:** **In the context of thermo-mechanical simulations, most of the calculation costs often come from the construction and resolution of linear systems**. Choosing the right linear solver is therefore essential, on the one hand for its speed, but also for its robustness and the memory space it requires. Each time, a compromise must be made between these constraints. For 60 years, two types of solvers have been competing for supremacy in the field, direct and iterative ones. Hence, as a precaution, a diversified offer of mechanical codes in this field. *code_aster* is no exception to the rule. It offers three direct solvers (Gauss [:external:ref:`R6.02.01 `], native multifrontend [:external:ref:`R6.02.02 `] and the external product MUMPS [:external:ref:`R6.02.03 `]), iterative Krylov-type solvers (GCPC Aster and all those from the PETSc library). **In this** **document**, **we detail** from a theoretical, algorithmic and *code_aster* modeling point of view, **the fundamentals of GCPC and the other Krylov solvers implemented in PETSc**. In particular, their links with other linear code solvers and continuous optimization methods are highlighted. We continue with their implementation difficulties, their settings, their perimeters as well as some tips for use. **For more details and advice** on the use of linear solvers, you can consult the specific instructions for use [:external:ref:`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 `] and [:external:ref:`U2.08.06 `]. .. toctree:: :hidden: self .. toctree:: :maxdepth: 2 :numbered: Probl_matique Les_m_thodes_de_descente Le_Gradient_Conjugu___GC_ Le_Gradient_Conjugu__Pr_Conditionn___GCPC_ Le_GCPC__natif__de_Code_Aster Les_solveurs_it_ratifs_de_Krylov_via_PETSc Traitement_des__checs Bibliographie Description_des_versions_du_document