For the solution of nonlinear equations resulting due to the implicit discretization of reservoir simulation partial differential equations, Newton's method has been an overwhelming choice. By providing robust and a considerably faster performance, the inexact Newton's methods offer attractive alternatives. Several Newton-Krylov inexact methods were examined for the solution of nonlinear equations arising in the finite-element discretization of a discrete-fracture reservoir simulation model. Two of the methods were found to be superior to the Newton's method. These techniques also had the additional advantage of being amenable to effective parallelization.

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