The Multigrid Preconditioned Conjugate Gradient Method
نویسنده
چکیده
multigrid method as a preconditioner of the PCG method, is proposed. The multigrid method has inherent high parallelism and improves convergence of long wave length components, which is important in iterative methods. By using this method as a preconditioner of the PCG method, an e cient method with high parallelism and fast convergence is obtained. First, it is considered a necessary condition of the multigrid preconditioner in order to satisfy requirements of a
منابع مشابه
Ecient Implementation of the Multigrid Preconditioned Conjugate Gradient Method on Distributed Memory Machines
A multigrid preconditioned conjugate gradient (MGCG) method[15], which uses the multigrid method as a preconditioner for the CG method, has a good convergence rate even for the problems on which the standard multigrid method does not converge efciently. This paper considers a parallelization of the MGCG method and proposes an e cient parallel MGCG method on distributed memory machines. For the ...
متن کاملcient Implementation of the Multigrid Preconditioned Conjugate Gradient Method on Distributed Memory
A multigrid preconditioned conjugate gradient (MGCG) method[15], which uses the multigrid method as a preconditioner for the CG method, has a good convergence rate even for the problems on which the standard multigrid method does not converge efciently. This paper considers a parallelization of the MGCG method and proposes an e cient parallel MGCG method on distributed memory machines. For the ...
متن کاملEfficient Solution of Symmetric Eigenvalue Problems Using Multigrid Preconditioners in the Locally Optimal Block Conjugate Gradient Method
We present a short survey of multigrid–based solvers for symmetric eigenvalue problems. We concentrate our attention on “of the shelf” and “black box” methods, which should allow solving eigenvalue problems with minimal, or no, effort on the part of the developer, taking advantage of already existing algorithms and software. We consider a class of such methods, where the multigrid only appears ...
متن کاملA fast algebraic multigrid preconditioned conjugate gradient solver
This work presents a new approach for selecting the coarse grids allowing a faster algebraic multigrid (AMG) preconditioned conjugate gradient solver. This approach is based on an appropriate choice of the parameter a considering the matrix density during the coarsening process which implies in a significant reduction in the matrix dimension at all AMG levels. 2005 Elsevier Inc. All rights rese...
متن کاملMultigrid and Krylov Subspace Methods for the Discrete Stokes Equations
Discretization of the Stokes equations produces a symmetric indefinite system of linear equations. For stable discretizatiom a variety of numerical methods have been proposed that have rates of convergence independent of the mesh size used in the dkretization. In this paper we compare the performance of four such methods, namely variants of the Uzawa, preconditioned conjugate gradient, precondi...
متن کاملAppendix 4.6.c a Multigrid Preconditioned Conjugate Gradient Method for Large Scale Wavefront Construction
We introduce a multigrid preconditioned conjugate gradient (MGCG) iterative scheme for computing open loop wavefront reconstructors in the adaptive optics (AO) system of large telescopes. We present numerical simulations which indicate that our MGCG method has a rapid convergence rate for a wide range of sub-aperture gradient measurement signal-to-noise ratios. The cost per iteration is order N...
متن کامل