Experimental study of the efficiency of solving 2D boundary value problems on subgrids of quasistructured rectangular grids

An experimental study of the solvers efficiency of 2D boundary value problems on subgrids of quasistructured rectangular grids was carried out. A solver is understood as a solution method and its software implementation. Three solvers are considered: one direct solver – the Buneman cyclic reduction method and two iterative ones: the Peaceman-Rachford method and the method of successive over relaxation. Characteristic features of the studies are: 1) the subgrids contain a small number of nodes, namely 8$\times$8, 16$\times$16, 32$\times$32, 64$\times$64; 2) the efficiency is estimated not only for single calculations, but also mainly for series of calculations, in each of which several repetitions of solving the problem with different boundary conditions on the same subgrid are carried out. Based on serial calculations, a combined method is proposed, and recommendations on the use of solvers are given.