Newton-Krylov Solvers for Time-Steppers
NORTH CAROLINA STATE UNIV AT RALEIGH CENTER FOR RESEARCH IN SCIENTIFIC COMPUTATION
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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.
- Theoretical Mathematics
- Numerical Mathematics