Preconditioning by fast direct methods for nonself-adjoint nonseparable elliptic equations
SIAM Journal on Numerical Analysis
GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Preconditioning and boundary conditions
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Optimal equivalent preconditioners
SIAM Journal on Numerical Analysis
Stabilization of unstable procedures: the recursive projection method
SIAM Journal on Numerical Analysis
An Adaptive Newton--Picard Algorithm with Subspace Iteration for Computing Periodic Solutions
SIAM Journal on Scientific Computing
Waveform Relaxation with Fast Direct Methods as Preconditioner
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Jacobian-free Newton-Krylov methods: a survey of approaches and applications
Journal of Computational Physics
Constraint-Defined Manifolds: a Legacy Code Approach to Low-Dimensional Computation
Journal of Scientific Computing
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
Mesh Independent Superlinear PCG Rates Via Compact-Equivalent Operators
SIAM Journal on Numerical Analysis
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We consider the computation of a fixed point of a time-stepper using Newton-Krylov methods, and propose and analyze equivalent operator preconditioning for the resulting linear systems. For a linear, scalar advection-reaction-diffusion equation, we investigate in detail how the convergence rate depends upon the choice of preconditioner parameters and upon the time discretization. The results are especially valuable when computing fixed points of a coarse time-stepper in the equation-free multiscale framework, in which one simulates an unavailable coarse-scale model by wrapping a set of computational routines around appropriately initialized fine-scale simulations. Both analytical results and numerical experiments are presented, showing that one can speed up the convergence of iterative methods significantly for a wide range of parameter values in the preconditioner.