A Nonlinear Additive Schwarz Preconditioned Inexact Newton Method for Shocked Duct Flow

A nonlinearly preconditioned inexact Newton algorithm (PIN) was recently introduced, in [CK00], for solving large sparse nonlinear system of equations arising from the discretization of nonlinear partial di erential equations. In PIN the nonlinear system F (u) = 0 is transformed into a new nonlinear system F(u) = 0, which has the same solution as the original system. For certain applications the nonlinearities of the new function F(u) are more balanced and, as a result, the inexact Newton method converges faster. In this paper, we shall use the nonlinear additive Schwarz algorithm as the preconditioner and focus on the performance of PIN for a compressible shock tube problem, which is known to be a diÆcult test case for inexact Newton type algorithms.

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