We propose a variant of the relaxation step used in the most widespread iterative methods (e.g. Jacobi Over-Relaxation, Successive Over-Relaxation) which combines the iteration at the predicted step, namely (n + 1), with the iteration at step (n - 1). We provide a theoretical analysis of the proposed algorithm by applying such a delayed relaxation step to a generic (convergent) iterative scheme. We prove that, under proper assumptions, this significantly improves the convergence rate of the initial iterative method. As a relevant example, we apply the proposed algorithm to the solution of the Poisson equation, highlighting the advantages in comparison with classical iterative models. (C) 2016 Elsevier Inc. All rights reserved.
Delayed Over-Relaxation for iterative methods
Antuono M;Colicchio G
2016
Abstract
We propose a variant of the relaxation step used in the most widespread iterative methods (e.g. Jacobi Over-Relaxation, Successive Over-Relaxation) which combines the iteration at the predicted step, namely (n + 1), with the iteration at step (n - 1). We provide a theoretical analysis of the proposed algorithm by applying such a delayed relaxation step to a generic (convergent) iterative scheme. We prove that, under proper assumptions, this significantly improves the convergence rate of the initial iterative method. As a relevant example, we apply the proposed algorithm to the solution of the Poisson equation, highlighting the advantages in comparison with classical iterative models. (C) 2016 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.