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Newton-Krylov solvers for time-steppers

C. T. Kelley·I. G. Kevrekidis·L. Qiao
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Abstract

We study how the Newton-GMRES iteration can enable dynamic simulators (time-steppers) to perform fixed-point and path-following computations.For a class of dissipative problems, whose dynamics are characterized by a slow manifold, the Jacobian matrices in such computations are compact perturbations of the identity. We examine the number of GMRES iterations required for each nonlinear iteration as a function of the dimension of the slow subspace and the time-stepper reporting horizon. In a path-following computation, only a small number (one or two) of additional GMRES iterations is required.

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C. T. Kelley, I. G. Kevrekidis, L. Qiao. 2004-04-21. Newton-Krylov solvers for time-steppers. https://arxiv.org/abs/math/0404374

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