A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

Yin Wang; Jeonghwa Lee; Jun Zhang

doi:10.1080/00207160701355938

A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

Yin Wang
, Jeonghwa Lee
, Jun Zhang

Computer Science

Research output: Contribution to journal › Review article › peer-review

8 Scopus citations

Abstract

In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.

Original language	English
Pages (from-to)	1211-1223
Number of pages	13
Journal	International Journal of Computer Mathematics
Volume	84
Issue number	8
DOIs	https://doi.org/10.1080/00207160701355938
State	Published - Aug 2007

Bibliographical note

Funding Information:
The research work of JZ was supported in part by the US National Science Foundation under grants CCR-0092532 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under grants KSEF-148-502-05-132 and KSEF-148-502-06-186, and in part by the Alzheimer’s Association under a New Investigator Research Grant NIGR-06-25460.

Funding

The research work of JZ was supported in part by the US National Science Foundation under grants CCR-0092532 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under grants KSEF-148-502-05-132 and KSEF-148-502-06-186, and in part by the Alzheimer’s Association under a New Investigator Research Grant NIGR-06-25460.

Funders	Funder number
National Science Foundation (NSF)	CCR-0092532, CCF-0527967
Alzheimer's Association	NIGR-06-25460
Kentucky Science and Engineering Foundation	KSEF-148-502-05-132, KSEF-148-502-06-186

Keywords

Dense matrices
Electromagnetics
Integral formulation
Multilevel fast multipole algorithm
Preconditioning techniques

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

Access to Document

10.1080/00207160701355938

Cite this

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title = "A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics",

abstract = "In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.",

keywords = "Dense matrices, Electromagnetics, Integral formulation, Multilevel fast multipole algorithm, Preconditioning techniques",

author = "Yin Wang and Jeonghwa Lee and Jun Zhang",

note = "Funding Information: The research work of JZ was supported in part by the US National Science Foundation under grants CCR-0092532 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under grants KSEF-148-502-05-132 and KSEF-148-502-06-186, and in part by the Alzheimer{\textquoteright}s Association under a New Investigator Research Grant NIGR-06-25460.",

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AU - Wang, Yin

AU - Lee, Jeonghwa

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N1 - Funding Information: The research work of JZ was supported in part by the US National Science Foundation under grants CCR-0092532 and CCF-0527967, in part by the Kentucky Science and Engineering Foundation under grants KSEF-148-502-05-132 and KSEF-148-502-06-186, and in part by the Alzheimer’s Association under a New Investigator Research Grant NIGR-06-25460.

PY - 2007/8

Y1 - 2007/8

N2 - In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.

AB - In solving systems of linear equations arising from practical scientific and engineering modelling and simulations such as electromagnetics applications, it is important to choose a fast and robust solver. Due to the large scale of those problems, preconditioned Krylov subspace methods are most suitable. In electromagnetics simulations, the use of preconditioned Krylov subspace methods in the context of multilevel fast multipole algorithms (MLFMA) is particularly attractive. In this paper, we present a short survey of a few preconditioning techniques in this application. We also compare several preconditioning techniques combined with the Krylov subspace methods to solve large dense linear systems arising from electromagnetic scattering problems and present some numerical results.

KW - Dense matrices

KW - Electromagnetics

KW - Integral formulation

KW - Multilevel fast multipole algorithm

KW - Preconditioning techniques

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U2 - 10.1080/00207160701355938

DO - 10.1080/00207160701355938

M3 - Review article

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JO - International Journal of Computer Mathematics

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A short survey on preconditioning techniques for large-scale dense complex linear systems in electromagnetics

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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