Adaptive GMRES(m) for the Electromagnetic Scattering Problem

Authors

  • Gustavo Espínola National University of Asuncion
  • Juan C. Cabral National University of Asuncion
  • Christian Schaerer Centro de Investigación en Matemática - CIMA

DOI:

https://doi.org/10.5540/tema.2020.021.01.191

Keywords:

Iterative method, adaptive GMRES(m), electromagnetic scattering

Abstract

In this article, an adaptive version of the restarted GMRES (GMRES(m)) is introduced for the resolution of the finite 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 fixed 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.

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Published

2020-03-27

How to Cite

Espínola, G., Cabral, J. C., & Schaerer, C. (2020). Adaptive GMRES(m) for the Electromagnetic Scattering Problem. Trends in Computational and Applied Mathematics, 21(1), 191. https://doi.org/10.5540/tema.2020.021.01.191

Issue

Vol. 21 No. 1 (2020)

Section

Original Article

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