GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

Kui Du

doi:10.1016/j.apnum.2011.04.003

GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

Kui Du

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

5 Citations (Scopus)

Abstract

GMRES with deflated restarting, denoted by GMRES-DR(m,k), is a variant of restarted GMRES for solving nonsymmetric linear systems, which improves the convergence of restarted GMRES by weakening the influence of the eigenvalues incurring poor numerical performance. However, it is difficult to determine the deflation parameter k. In this paper, we present a new deflation strategy which determines k dynamically in different cycles. Numerical results for an electromagnetic cavity problem show that the deflation strategy is efficient. © 2011 IMACS.

Original language	English
Pages (from-to)	977-988
Journal	Applied Numerical Mathematics
Volume	61
Issue number	9
DOIs	https://doi.org/10.1016/j.apnum.2011.04.003
Publication status	Published - Sept 2011

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

The research of the author was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 103410), the Academy of Finland grant 128474 and the Väisälä Foundation of the Finnish Academy of Science and Letters.

Research Keywords

Deflation strategy
Electromagnetic scattering
GMRES-DR

RGC Funding Information

RGC-funded

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10.1016/j.apnum.2011.04.003

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title = "GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem",

abstract = "GMRES with deflated restarting, denoted by GMRES-DR(m,k), is a variant of restarted GMRES for solving nonsymmetric linear systems, which improves the convergence of restarted GMRES by weakening the influence of the eigenvalues incurring poor numerical performance. However, it is difficult to determine the deflation parameter k. In this paper, we present a new deflation strategy which determines k dynamically in different cycles. Numerical results for an electromagnetic cavity problem show that the deflation strategy is efficient. {\textcopyright} 2011 IMACS.",

keywords = "Deflation strategy, Electromagnetic scattering, GMRES-DR",

author = "Kui Du",

note = "Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].",

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language = "English",

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T1 - GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

AU - Du, Kui

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2011/9

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N2 - GMRES with deflated restarting, denoted by GMRES-DR(m,k), is a variant of restarted GMRES for solving nonsymmetric linear systems, which improves the convergence of restarted GMRES by weakening the influence of the eigenvalues incurring poor numerical performance. However, it is difficult to determine the deflation parameter k. In this paper, we present a new deflation strategy which determines k dynamically in different cycles. Numerical results for an electromagnetic cavity problem show that the deflation strategy is efficient. © 2011 IMACS.

AB - GMRES with deflated restarting, denoted by GMRES-DR(m,k), is a variant of restarted GMRES for solving nonsymmetric linear systems, which improves the convergence of restarted GMRES by weakening the influence of the eigenvalues incurring poor numerical performance. However, it is difficult to determine the deflation parameter k. In this paper, we present a new deflation strategy which determines k dynamically in different cycles. Numerical results for an electromagnetic cavity problem show that the deflation strategy is efficient. © 2011 IMACS.

KW - Deflation strategy

KW - Electromagnetic scattering

KW - GMRES-DR

UR - https://www.scopus.com/pages/publications/79957850297

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-79957850297&origin=recordpage

U2 - 10.1016/j.apnum.2011.04.003

DO - 10.1016/j.apnum.2011.04.003

M3 - RGC 21 - Publication in refereed journal

SN - 0168-9274

VL - 61

SP - 977

EP - 988

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 9

ER -

GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

Abstract

Bibliographical note

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Research Keywords

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GRF: Spectral Galerkin/Collocation Methods for Helmholtz Equations and Applications

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GMRES with adaptively deflated restarting and its performance on an electromagnetic cavity problem

Abstract

Bibliographical note

Funding

Research Keywords

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

Fingerprint

Projects

GRF: Spectral Galerkin/Collocation Methods for Helmholtz Equations and Applications

Cite this