1. A method for conducting a reservoir simulation, comprising the steps of: a. building a reservoir model, of a region of interest, by gridding the region of interest, the grid being comprised of one or more types of cells, the types of cell being distinguished by the number of unknown variables representing properties of the cells, but with each cell having a common variable as an unknown variable; b. identifying different cell types for the grid; c. constructing an overall matrix for the reservoir model based on the different cell types; d. at least partially decoupling the common variable from the other unknown variables in the matrix by using a reduction process to yield a reduced matrix; e. mathematically breaking up the variables in the reduced matrix into k subsets by cell types f. and applying an overlapping multiplicative Schwartz procedure to the reduced matrix to obtain a preconditioner.