IEICE TRANSACTIONS on Electronics
Acceleration of Flexible GMRES Using Fast Multipole Method for Implementation Based on Combined Tangential Formulation
Summary :
In this study, we demonstrate an acceleration of flexible generalized minimal residual algorithm (FGMRES) implemented with the method of moments and the fast multipole method (FMM), based on a combined tangential formulation. For the implementation of the FGMRES incorporated with the FMM concept, we propose a new definition of the truncation number for the FMM operator within the inner solver. The proposed truncation number provides an optimal variable preconditioner by controlling the accuracy and computational cost of the inner iteration. Moreover, to further accelerate the convergence, we introduce the concept of a multistage preconditioner. Numerical experiments reveal that our new version of FGMRES, based on the proposed truncation number for the inner solver and the multistage preconditioner, achieves outstanding acceleration of the convergence for large-scale and practical electromagnetic scattering and radiation problems with several levels of geometrical complexity.
- Publication
- IEICE TRANSACTIONS on Electronics Vol.E94-C No.10 pp.1661-1668
- Publication Date
- 2011/10/01
- Publicized
- Online ISSN
- 1745-1353
- DOI
- 10.1587/transele.E94.C.1661
- Type of Manuscript
- PAPER
- Category
- Electromagnetic Theory
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Keyword
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Hidetoshi CHIBA, Toru FUKASAWA, Hiroaki MIYASHITA, Yoshihiko KONISHI, "Acceleration of Flexible GMRES Using Fast Multipole Method for Implementation Based on Combined Tangential Formulation" in IEICE TRANSACTIONS on Electronics,
vol. E94-C, no. 10, pp. 1661-1668, October 2011, doi: 10.1587/transele.E94.C.1661.
Abstract: In this study, we demonstrate an acceleration of flexible generalized minimal residual algorithm (FGMRES) implemented with the method of moments and the fast multipole method (FMM), based on a combined tangential formulation. For the implementation of the FGMRES incorporated with the FMM concept, we propose a new definition of the truncation number for the FMM operator within the inner solver. The proposed truncation number provides an optimal variable preconditioner by controlling the accuracy and computational cost of the inner iteration. Moreover, to further accelerate the convergence, we introduce the concept of a multistage preconditioner. Numerical experiments reveal that our new version of FGMRES, based on the proposed truncation number for the inner solver and the multistage preconditioner, achieves outstanding acceleration of the convergence for large-scale and practical electromagnetic scattering and radiation problems with several levels of geometrical complexity.
URL: https://global.ieice.org/en_transactions/electronics/10.1587/transele.E94.C.1661/_p
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@ARTICLE{e94-c_10_1661,
author={Hidetoshi CHIBA, Toru FUKASAWA, Hiroaki MIYASHITA, Yoshihiko KONISHI, },
journal={IEICE TRANSACTIONS on Electronics},
title={Acceleration of Flexible GMRES Using Fast Multipole Method for Implementation Based on Combined Tangential Formulation},
year={2011},
volume={E94-C},
number={10},
pages={1661-1668},
abstract={In this study, we demonstrate an acceleration of flexible generalized minimal residual algorithm (FGMRES) implemented with the method of moments and the fast multipole method (FMM), based on a combined tangential formulation. For the implementation of the FGMRES incorporated with the FMM concept, we propose a new definition of the truncation number for the FMM operator within the inner solver. The proposed truncation number provides an optimal variable preconditioner by controlling the accuracy and computational cost of the inner iteration. Moreover, to further accelerate the convergence, we introduce the concept of a multistage preconditioner. Numerical experiments reveal that our new version of FGMRES, based on the proposed truncation number for the inner solver and the multistage preconditioner, achieves outstanding acceleration of the convergence for large-scale and practical electromagnetic scattering and radiation problems with several levels of geometrical complexity.},
keywords={},
doi={10.1587/transele.E94.C.1661},
ISSN={1745-1353},
month={October},}
Copy
TY - JOUR
TI - Acceleration of Flexible GMRES Using Fast Multipole Method for Implementation Based on Combined Tangential Formulation
T2 - IEICE TRANSACTIONS on Electronics
SP - 1661
EP - 1668
AU - Hidetoshi CHIBA
AU - Toru FUKASAWA
AU - Hiroaki MIYASHITA
AU - Yoshihiko KONISHI
PY - 2011
DO - 10.1587/transele.E94.C.1661
JO - IEICE TRANSACTIONS on Electronics
SN - 1745-1353
VL - E94-C
IS - 10
JA - IEICE TRANSACTIONS on Electronics
Y1 - October 2011
AB - In this study, we demonstrate an acceleration of flexible generalized minimal residual algorithm (FGMRES) implemented with the method of moments and the fast multipole method (FMM), based on a combined tangential formulation. For the implementation of the FGMRES incorporated with the FMM concept, we propose a new definition of the truncation number for the FMM operator within the inner solver. The proposed truncation number provides an optimal variable preconditioner by controlling the accuracy and computational cost of the inner iteration. Moreover, to further accelerate the convergence, we introduce the concept of a multistage preconditioner. Numerical experiments reveal that our new version of FGMRES, based on the proposed truncation number for the inner solver and the multistage preconditioner, achieves outstanding acceleration of the convergence for large-scale and practical electromagnetic scattering and radiation problems with several levels of geometrical complexity.
ER -
English
