@inbook{c63889d8a3914559bc73d4f14aa7ddfd,
title = "On acceleration of krylov-subspace-based newton and arnoldi iterations for incompressible CFD: Replacing time steppers and generation of initial guess",
abstract = "We propose two techniques aimed at improving the convergence rate of steady state and eigenvalue solvers preconditioned by the inverse Stokes operator and realized via time-stepping. First, we suggest a generalization of the Stokes operator so that the resulting preconditioner operator depends on several parameters and whose action preserves zero divergence and boundary conditions. The parameters can be tuned for each problem to speed up the convergence of a Krylov-subspace-based linear algebra solver. This operator can be inverted by the Uzawa-like algorithm, and does not need a time-stepping. Second, we propose to generate an initial guess of steady flow, leading eigenvalue and eigenvector using orthogonal projection on a divergence-free basis satisfying all boundary conditions. The approach, including the two proposed techniques, is illustrated on the solution of the linear stability problem for laterally heated square and cubic cavities.",
keywords = "CFD, Eigenvalue solver, Krylov methods, Linear stability, Newton solver",
author = "Alexander Gelfgat",
note = "Publisher Copyright: {\textcopyright} 2019, Springer International Publishing AG, part of Springer Nature. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2019",
doi = "10.1007/978-3-319-91494-7_5",
language = "אנגלית",
series = "Computational Methods in Applied Sciences",
publisher = "Springer Netherland",
pages = "147--167",
booktitle = "Computational Methods in Applied Sciences",
}