A multigrid conjugate gradient method

Authors:
Christoph Pflaum
Affiliations:
University Erlangen-Nürnberg, Institute of Computer Science, Cauerstraße 6, 91058 Erlangen, Germany
Venue:
Applied Numerical Mathematics
Year:
2008

Citing 4
Cited 0

Iterative methods by space decomposition and subspace correction

SIAM Review
Iterative solution methods

Iterative solution methods
Multigrid Method for Maxwell's Equations

SIAM Journal on Numerical Analysis
Problem dependent generalized prewavelets

Computing

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, we describe a new approach to combine the conjugate gradient method and the multigrid method. This approach simultaneously constructs conjugate new correction directions based on restricted gradients. The computational amount is O(N), where N is the number of unknowns. The algorithm is easy to implement. It only requires restriction and prolongation operators, matrix vector multiplications on several levels, and scalar products. Therefore, the algorithm can be applied to accelerate a multilevel algorithm with slow convergence. Numerical results for Poisson's equation with jumping coefficients and a Stokes type equation are presented.