A method of computerized simulation of a giant subsurface reservoir in a data processing system of a plurality of data processors, the computerized simulation being an iterative linear solution of equations for reservoir parameters of a giant subsurface reservoir, the giant subsurface reservoir being simulated as a model partitioned into a number of cells arranged in an organized system of cells, the simulation further being based on geological and fluid characterization information for the cells of the reservoir, the method comprising the computer processing steps of: mapping information from the organized system of cells of the reservoir from an original fine grid scale into a coarse cell grid of a reduced number from the original grid; characterized in that it further comprising the computer processing steps of: initializing a postulated system solution matrix in the computer system for reservoir parameters for the coarse cell grid, comprising: setting an estimate of matrix values for each cell of a first set (C 1) of alternately spaced cells of the coarse cell grid equal to zero; and setting an estimate of matrix values for each cell of a second set (C 2) of alternately spaced cells of the coarse cell grid, which are adjacent the alternately spaced cells of the first set (C 1) of the coarse cell grid, such that residual matrix values of the second set (C 2) of alternately spaced cells of the coarse cell grid are equal to zero. performing a preconditioned conjugate-gradient extrapolation in the computer system on the initialized postulated system solution matrix for the coarse cell grid, the preconditioned conjugate-gradient extrapolation comprising: performing a solution for the matrix values for the first set (C 1) of alternately spaced cells of the coarse cell grid without computing updates to the residual matrix values of the second set (C 2) of alternately spaced cells of the coarse cell grid; and performing a solution for the matrix values for the second set (C 2) of alternately spaced cells of the coarse cell grid; transforming in the computer system the results of the preconditioned conjugate-gradient extrapolation for the coarse cell grid to the original cell grid; and performing an iterative linear solution in the computer system for reservoir parameters for the original grid of cells. mapping information from the organized system of cells of the reservoir from an original fine grid scale into a coarse cell grid of a reduced number from the original grid; initializing a postulated system solution matrix in the computer system for reservoir parameters for the coarse cell grid, comprising: setting an estimate of matrix values for each cell of a first set (C 1) of alternately spaced cells of the coarse cell grid equal to zero; and setting an estimate of matrix values for each cell of a second set (C 2) of alternately spaced cells of the coarse cell grid, which are adjacent the alternately spaced cells of the first set (C 1) of the coarse cell grid, such that residual matrix values of the second set (C 2) of alternately spaced cells of the coarse cell grid are equal to zero. setting an estimate of matrix values for each cell of a first set (C 1) of alternately spaced cells of the coarse cell grid equal to zero; and setting an estimate of matrix values for each cell of a second set (C 2) of alternately spaced cells of the coarse cell grid, which are adjacent the alternately spaced cells of the first set (C 1) of the coarse cell grid, such that residual matrix values of the second set (C 2) of alternately spaced cells of the coarse cell grid are equal to zero. performing a preconditioned conjugate-gradient extrapolation in the computer system on the initialized postulated system solution matrix for the coarse cell grid, the preconditioned conjugate-gradient extrapolation comprising: performing a solution for the matrix values for the first set (C 1) of alternately spaced cells of the coarse cell grid without computing updates to the residual matrix values of the second set (C 2) of alternately spaced cells of the coarse cell grid; and performing a solution for the matrix values for the second set (C 2) of alternately spaced cells of the coarse cell grid; performing a solution for the matrix values for the first set (C 1) of alternately spaced cells of the coarse cell grid without computing updates to the residual matrix values of the second set (C 2) of alternately spaced cells of the coarse cell grid; and performing a solution for the matrix values for the second set (C 2) of alternately spaced cells of the coarse cell grid; transforming in the computer system the results of the preconditioned conjugate-gradient extrapolation for the coarse cell grid to the original cell grid; and performing an iterative linear solution in the computer system for reservoir parameters for the original grid of cells.