| TWO-STAGE PRECONDITIONERS FOR INEXACT NEWTON METHODS IN MULTI-PHASE RESERVOIR SIMULATION (2007) | |||||||||||||||
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| Abstract. 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. Keywords: Two-stage methods, preconditioners, Krylov iterative solvers, block methods, coupled nonlinear partial differential equations, inexact Newton methods, multi-phase flow and transport, reservoir simulation. AMS(MOS) subject classification: 3504, 35Q35, 35M10 | |||||||||||||||
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