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