It is widely known, that modern supercomputers contain thousands of computational nodes and co-processors. Making this power work for our needs requires exploiting effective parallel methods and programs, including programs for solving systems of linear algebraic equations. This article presents a review of PMLP/ParSol library and "LOGOS.Aerohydromechanics" package, which allow such computations, using MPI and OpenMP facilities. The results of experiments in problems of heat diffusion, viscid turbulent gas flow, solid body distortion, fluid diffusion in porous medium, production rate simulations are shown. The number of utilized computational cores is approximately 10 4. The main methods of parallel SLAE solving, which are implemented in LParSol, are parallel Schwartz method (MPI and OpenMP variants) and algebraic multigrid method (AMG, selective and aggregative). Preconditioned solvers like CG and BiCGStab are used as iterative solvers. Different versions of incomplete ILU/IC factorization are used as preconditioners. One of the main advantages of PMLP/ParSol library is the ability of utilizing structures, which remain the same on the flow of SLAEs. This allows reducing computational overhead for building a preconditioner, for example. Moreover, there is an option of adaptive solver adjustment for SLAEs in the flow, while their difficulty is changing. The results of experiments presented show, that PMLP/ParSol library is suitable for solving SLAEs, which arise from problems of different computational mathematics fields. LParSol library complex is used in lots of program packages of Russian Federal Nuclear Center-All-Russian Research Institute of Experimental Physics.