REPEATED USE OF A HIERARCHICAL DATA STRUCTURE IN AN ALGEBRAIC MULTIGRID SOLVER FOR SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS
Yu. G. Bartenev, A. P. Karpov
VANT. Ser.: Mat. Mod. Fiz. Proc 2019. Вып.4. С. 66-77.
Repeated use of a hierarchical data structure generated in an algebraic multigrid preconditioner and solver for a series of SLAEs with the same matrix profile is considered. This approach, called partial construction of a multigrid algebraic solver fully pre-constructed for a previous SLAE, involves updating merely the coefficients of the pre-constructed coarse matrices without changing their structure. Examples of using a combination of full and partial construction of an algebraic multigrid solver in different modifications of its implementation are given. This solver construction approach in the PMLP/ParSol and some other libraries is shown to considerably reduce the time of solving SLAEs in simulations of different physical processes. The issue of adaptive combination of full and partial algebraic multigrid solver construction is discussed in brief. Keywords: system of linear algebraic equations, sparse matrices, algebraic multigrid preconditioners and solvers, hydrodynamic equations, aerodynamic equations, equations of heat transfer in solids, equations of liquid diffusion in porous media, equations of radiant heat transfer, series of SLAEs with the same matrix profile, iterative solvers ÑG, BiCGStab.
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