Open AccessAdaptive GMRES(m) for the Electromagnetic Scattering Problem
Author(s) -
Gustavo Espínola,
Juan C. Cabral,
Christian E. Schaerer
Publication year - 2020
Publication title -
tema
Language(s) - English
Resource type - Journals
eISSN - 2179-8451
pISSN - 1677-1966
DOI - 10.5540/tema.2020.021.01.191
Subject(s) - generalized minimal residual method , krylov subspace , mathematics , convergence (economics) , mathematical optimization , computer science , iterative method , algorithm , economics , economic growth
In this article, an adaptive version of the restarted GMRES (GMRES(m)) is introduced for the resolution of the nite difference approximation of the Helmholtz equation. It has been observed that the choice of the restart parameter m strongly affects the convergence of standard GMRES(m). To overcome this problem, the GMRES(m) is formulated as a control problem in order to adaptively combine two strategies: a) the appropriate variation of the restarted parameter m, if a stagnation in the convergence is detected; and b) the augmentation of the search subspace using vectors obtained at previous cycles. The proposal is compared with similar iterative methods of the literature based on standard GMRES(m) with xed parameters. Numerical results for selected matrices suggest that the switching adaptive proposal method could overcome the stagnation observed in standard methods, and even improve the performance in terms of computational time and memory requirements.