Generalities
===========

This command allows you to solve:


*
    *
        * by a direct method, the linear system :math:`\mathrm{AX}=B`, where :math:`A` is a matrix previously "factorized" by the command FACTORISER [:external:ref:`U4.51.01. <U4.51.01.>`],


        * by an iterative method (GCPC or PETSC), the linear system :math:`{P}^{-1}\mathrm{AX}={P}^{-1}B`, where :math:`{P}^{-1}` is a pre-conditioning matrix determined by the command FACTORISER [:ref:`U4.51.01 <U4.51.01>`] and :math:`A` the initial assembled matrix.

Resolution is possible for dualized or eliminated Dirichlet boundary conditions (kinematic boundary conditions) [:ref:`U2.01.02 <U2.01.02>`]. In the latter case, if the load :math:`\mathrm{X}={\mathrm{X}}_{0}` on the "edge" :math:`{\Gamma }_{0}` is applied with a kinematic load (operator AFFE_CHAR_CINE [:external:ref:`U4.44.03 <U4.44.03>`]) taken into account in the assembled matrix (operator ASSE_MATRICE [:external:ref:`U4.61.22 <U4.61.22>`]), the "value" of this load :math:`({X}_{0})`, calculated by the operator CALC_CHAR_CINE [:external:ref:`U4.61.03 <U4.61.03>`] must be provided by the CHAM_CINE keyword.