CRPC-TR96641-S: Two-Stage Preconditioners for Inexact Newton Methods
in Multi-phase Reservoir Simulation

Hector Klie, Marcelo Rame, Mary Wheeler

January, 1996

Two-stage procedures refers to a family of convergent nested or
inner-outer iterations. This paper addresses their use as
preconditioners in the context of systems of coupled nonlinear partial
differential equations, specifically those modeling underground
multiphase flow phenomena. The linear systems arising after the
discretization and the Newton linearization are highly nonsymmetric
and indefinite but coefficient blocks associated with a particular
type of unknown possess properties that can be exploited to enhance
the overall conditioning of the coupled system. We show that
decoupling strategies combined with two-stage preconditioners provide
an efficient device to accelerate Krylov subspace methods such as
GMRES\ and BiCGSTAB. Theoretical discussion and numerical experiments
reveal the suitability of this approach and contrast it to fairly
robust, standard ones which ``blindly'' precondition the entire
coupled linear system.