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Volume 32, Issue 2
Numerical Studies of a Class of Composite Preconditioners

Qiang Niu & Michael Ng

DOI: 10.4208/jcm.1401-m4145

J. Comp. Math., 32 (2014), pp. 136-151.

Published online: 2014-04

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  • Abstract

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 $\mathcal{O}$($h^{-\frac23}_p$) 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.

  • Keywords

Preconditioner, ILU, Tangential frequency filtering decomposition, GMRES.

  • AMS Subject Headings

65F10, 65N22.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-32-136, author = {Qiang Niu and Michael Ng}, title = {Numerical Studies of a Class of Composite Preconditioners}, journal = {Journal of Computational Mathematics}, year = {2014}, volume = {32}, number = {2}, pages = {136--151}, abstract = {

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 $\mathcal{O}$($h^{-\frac23}_p$) 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1401-m4145}, url = {http://global-sci.org/intro/article_detail/jcm/9874.html} }
TY - JOUR T1 - Numerical Studies of a Class of Composite Preconditioners AU - Qiang Niu & Michael Ng JO - Journal of Computational Mathematics VL - 2 SP - 136 EP - 151 PY - 2014 DA - 2014/04 SN - 32 DO - http://doi.org/10.4208/jcm.1401-m4145 UR - https://global-sci.org/intro/article_detail/jcm/9874.html KW - Preconditioner, ILU, Tangential frequency filtering decomposition, GMRES. AB -

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 $\mathcal{O}$($h^{-\frac23}_p$) 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.

Qiang Niu and Michael Ng. (2014). Numerical Studies of a Class of Composite Preconditioners. Journal of Computational Mathematics. 32 (2). 136-151. doi:10.4208/jcm.1401-m4145
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