Krylov Subspace Acceleration of Nonlinear Multigrid with Application to Recirculating Flows
نویسندگان
چکیده
This paper deals with the combination of two solution methods: multigrid and GMRES [SIAM J. Sci. Comput., 14 (1993), pp. 856–869]. The generality and parallelizability of this combination are established by applying it to systems of nonlinear PDEs. As the “preconditioner” for a nonlinear Krylov subspace method, we use the full approximation storage (FAS) scheme [Math. Comp., 31 (1977), pp. 333–390], a nonlinear multigrid method. The nonlinear Krylov acceleration is applied also on coarse grids, so that recirculating incompressible flow problems discretized with a higher order upwind scheme can be solved efficiently.
منابع مشابه
Krylov Subspace Acceleration for Nonlinear Multigrid Schemes∗
In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a ‘preconditioner’ we use nonlinear multigrid schemes such as the Full Approximation Scheme (FAS) [1]. The benefits of nonlinear multigrid used in combination with the new accelerator are illustrated by difficult nonlinear elliptic scalar problems, such as the Bratu problem, and for systems of nonlinear equations, s...
متن کاملKrylov Subspace Acceleration Method for Nonlinear Multigrid Schemes
In this paper we present a Krylov acceleration technique for nonlinear PDEs. As a `precon-ditioner' we use nonlinear multigrid schemes, like FAS 1]. The beneets of the combination of nonlinear multigrid and the new proposed accelerator is shown for diicult nonlinear ellip-tic scalar problems, like the Bratu problem and for systems of nonlinear equations, like the Navier-Stokes equations.
متن کاملOn a Multilevel Krylov Method for the Helmholtz Equation Preconditioned by Shifted Laplacian
In Erlangga and Nabben [SIAM J. Sci. Comput., 30 (2008), pp. 1572–1595], a multilevel Krylov method is proposed to solve linear systems with symmetric and nonsymmetric matrices of coefficients. This multilevel method is based on an operator which shifts some small eigenvalues to the largest eigenvalue, leading to a spectrum which is favorable for convergence acceleration of a Krylov subspace me...
متن کاملAcceleration Methods for Total Variation-Based Image Denoising
For a given blur, we apply a fixed point method to solve the total variation-based image restoration problem. A new algorithm for the discretized system is presented. Convergence of outer iteration is efficiently improved by adding a linear term on both sides of the system of nonlinear equations. In inner iteration, an algebraic multigrid (AMG) method is applied to solve the linearized systems ...
متن کاملA Multigrid-Preconditioned Newton-Krylov Method for the Incompressible Navier-Stokes Equations
Globalized inexact Newton methods are well suited for solving large-scale systems of nonlinear equations. When combined with a Krylov iterative method, an explicit Jacobian is never needed, and the resulting matrix-free Newton–Krylov method greatly simplifies application of the method to complex problems. Despite asymptotically superlinear rates of convergence, the overall efficiency of a Newto...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Scientific Computing
دوره 21 شماره
صفحات -
تاریخ انتشار 2000