Using spectral low rank preconditioners for large electromagnetic calculations

Duff, IS; Giraud, Luc; Langou, Julien; Martin, E. Dale

doi:10.1002/nme.1201

Cited by 18 publications

(18 citation statements)

References 17 publications

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“…Similar types of composite preconditioners have been discussed in [23,29,35,36,38,44,45]. Here we mention that the preconditioners based on alternative direction iterations [14,41,46] can also be classified as such kind of composite preconditioners.…”

Section: Fourier Analysis Of the Composite Preconditionermentioning

confidence: 92%

“…However, these approaches may become ineffective when dealing with general sparse systems of linear equations. Another type of efficient preconditioning techniques are constructed by making use of spectrum information of the preconditioned matrix [23,29,38,44,45]. They are able to get rid of the influence of eigenvalues close to zero, which is generally difficult to handle by conventional incomplete factorization preconditioners.…”

Section: Introductionmentioning

confidence: 99%

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Numerical Studies of a Class of Composite Preconditioners

Niu

Ng²

2014

JCM

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In this paper, we study a composite preconditioner that combines the modified tangential frequency filtering decomposition with the ILU(0) factorization. Spectral property of the composite preconditioner is examined by the approach of Fourier analysis. We illustrate that condition number of the preconditioned matrix by the composite preconditioner is asymptotically bounded by O(h − 2 3 p ) on a standard model problem. Performance of the composite preconditioner is compared with other preconditioners on several problems arising from the discretization of PDEs with discontinuous coefficients. Numerical results show that performance of the proposed composite preconditioner is superior to other relative preconditioners.Mathematics subject classification: 65F10, 65N22.

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Section: Fourier Analysis Of the Composite Preconditionermentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

Numerical Studies of a Class of Composite Preconditioners

Niu

Ng²

2014

JCM

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“…Recently, the development and practice of efficient preconditioning techniques in iteratively solving dense linear systems have become the subject of growing interest [9,[22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37]. For sparse matrices, polynomial preconditioners for Krylov subspace methods were popular for some applications in the early stage of preconditioning studies [38,39].…”

Section: Preconditioned Iterative Methodsmentioning

confidence: 99%

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

Wang

Lee

Zhang

2007

International Journal of Computer Mathematics

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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.

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“…We should mention that there are other studies in the context of MLFMA that make use of both near-field and far-field information [19], [20]. In those studies, spectral information is explicitly computed via iterative eigensystem solvers and then this information is used to obtain a two-level preconditioner.…”

Section: B Preconditioners Using Far-field Interactionsmentioning

confidence: 99%

Sequential and parallel preconditioners for large-scale integral-equation problems

Malas

Ergül

Gürel

2007

2007 Computational Electromagnetics Workshop

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For efficient solutions of integral-equation methods via the multilevel fast multipole algorithm (MLFMA), effective preconditioners are required. In this paper we review appropriate preconditioners that have been used for sparse systems and developed specially in the context of MLFMA. First we review the ILU-type preconditioners that are suitable for sequential implementations. We can make these preconditioners robust and efficient for integral-equation methods by making appropriate selections and by employing pivoting to suppress the instability problem. For parallel implementations, the sparse approximate inverse or the iterative solution of the near-field system enables fast convergence up to certain problem sizes. However, for very large problems, the near-field matrix itself becomes insufficient to approximate the dense system matrix and preconditioners generated from the near-field interactions cannot be effective. Therefore, we propose an approximation strategy to MLFMA to be used as an effective preconditioner. Our numerical experiments reveal that this scheme significantly outperforms other preconditioners. With the combined effort of effective preconditioners and an efficiently parallelized MLFMA, we are able to solve problems with tens of millions of unknowns in a few hours. We report the solution of integral-equation problems that are among the largest in their classes.

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Using spectral low rank preconditioners for large electromagnetic calculations

Cited by 18 publications

References 17 publications

Numerical Studies of a Class of Composite Preconditioners

Numerical Studies of a Class of Composite Preconditioners

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

Sequential and parallel preconditioners for large-scale integral-equation problems

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