The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems

Reinaldo Astudillo Rengifo; Martin van Gijzen

doi:10.1007/978-3-319-39929-4_29

The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems

Reinaldo Astudillo Rengifo, Martin van Gijzen

Numerical Analysis

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

1 Citation (Scopus)

Abstract

Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax=b.
In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, SIAM J Sci Comput 31(2):1035–1062, 2008), with other short-recurrences Krylov methods, specifically the Bi-Conjugate Gradient Method (Bi-CG) (Fletcher, Conjugate gradient methods for indefinite systems. In: Proceedings of the Dundee conference on numerical analysis, pp 73–89, 1976), restarted Generalized Minimal Residual (GMRES(m)) (Saad and Schultz, SIAM J Sci Stat Comput 7:856–869, 1986), and Bi-Conjugate Gradient Stabilized method (Bi-CGSTAB) (van der Vorst, SIAM J Sci Stat Comput 13(2):631–644, 1992).

Original language	English
Title of host publication	Numerical Mathematics and Advanced Applications ENUMATH 2015
Editors	B. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, Ö. Uğur
Publisher	Springer
Pages	295-303
Number of pages	9
ISBN (Electronic)	978-3-319-39929-4
DOIs	https://doi.org/10.1007/978-3-319-39929-4_29
Publication status	Published - 2016
Event	ENUMATH 2015: The European Conference on Numerical Mathematics and Advanced Applications - Ankara, Turkey Duration: 14 Sept 2015 → 18 Sept 2015

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	112

Conference

Conference	ENUMATH 2015
Country/Territory	Turkey
City	Ankara
Period	14/09/15 → 18/09/15

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10.1007/978-3-319-39929-4_29

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Astudillo Rengifo, R., & van Gijzen, M. (2016). The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems. In B. Karasözen, M. Manguoğlu, M. Tezer-Sezgin, S. Göktepe, & Ö. Uğur (Eds.), Numerical Mathematics and Advanced Applications ENUMATH 2015 (pp. 295-303). (Lecture Notes in Computational Science and Engineering; Vol. 112). Springer. https://doi.org/10.1007/978-3-319-39929-4_29

Astudillo Rengifo, Reinaldo ; van Gijzen, Martin. / The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems. Numerical Mathematics and Advanced Applications ENUMATH 2015. editor / B. Karasözen ; M. Manguoğlu ; M. Tezer-Sezgin ; S. Göktepe ; Ö. Uğur. Springer, 2016. pp. 295-303 (Lecture Notes in Computational Science and Engineering).

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title = "The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems",

abstract = "Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax=b.In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, SIAM J Sci Comput 31(2):1035–1062, 2008), with other short-recurrences Krylov methods, specifically the Bi-Conjugate Gradient Method (Bi-CG) (Fletcher, Conjugate gradient methods for indefinite systems. In: Proceedings of the Dundee conference on numerical analysis, pp 73–89, 1976), restarted Generalized Minimal Residual (GMRES(m)) (Saad and Schultz, SIAM J Sci Stat Comput 7:856–869, 1986), and Bi-Conjugate Gradient Stabilized method (Bi-CGSTAB) (van der Vorst, SIAM J Sci Stat Comput 13(2):631–644, 1992).",

author = "{Astudillo Rengifo}, Reinaldo and {van Gijzen}, Martin",

year = "2016",

doi = "10.1007/978-3-319-39929-4_29",

language = "English",

series = "Lecture Notes in Computational Science and Engineering",

publisher = "Springer",

pages = "295--303",

editor = "B. Karas{\"o}zen and M. Manguoğlu and M. Tezer-Sezgin and S. G{\"o}ktepe and {\"O}. Uğur",

booktitle = "Numerical Mathematics and Advanced Applications ENUMATH 2015",

note = "ENUMATH 2015 : The European Conference on Numerical Mathematics and Advanced Applications ; Conference date: 14-09-2015 Through 18-09-2015",

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Astudillo Rengifo, R & van Gijzen, M 2016, The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems. in B Karasözen, M Manguoğlu, M Tezer-Sezgin, S Göktepe & Ö Uğur (eds), Numerical Mathematics and Advanced Applications ENUMATH 2015. Lecture Notes in Computational Science and Engineering, vol. 112, Springer, pp. 295-303, ENUMATH 2015, Ankara, Turkey, 14/09/15. https://doi.org/10.1007/978-3-319-39929-4_29

The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems. / Astudillo Rengifo, Reinaldo; van Gijzen, Martin.
Numerical Mathematics and Advanced Applications ENUMATH 2015. ed. / B. Karasözen; M. Manguoğlu; M. Tezer-Sezgin; S. Göktepe; Ö. Uğur. Springer, 2016. p. 295-303 (Lecture Notes in Computational Science and Engineering; Vol. 112).

Research output: Chapter in Book/Conference proceedings/Edited volume › Conference contribution › Scientific › peer-review

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AU - van Gijzen, Martin

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N2 - Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax=b.In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, SIAM J Sci Comput 31(2):1035–1062, 2008), with other short-recurrences Krylov methods, specifically the Bi-Conjugate Gradient Method (Bi-CG) (Fletcher, Conjugate gradient methods for indefinite systems. In: Proceedings of the Dundee conference on numerical analysis, pp 73–89, 1976), restarted Generalized Minimal Residual (GMRES(m)) (Saad and Schultz, SIAM J Sci Stat Comput 7:856–869, 1986), and Bi-Conjugate Gradient Stabilized method (Bi-CGSTAB) (van der Vorst, SIAM J Sci Stat Comput 13(2):631–644, 1992).

AB - Discretization of (linearized) convection-diffusion-reaction problems yields a large and sparse non symmetric linear system of equations, Ax=b.In this work, we compare the computational behavior of the Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, SIAM J Sci Comput 31(2):1035–1062, 2008), with other short-recurrences Krylov methods, specifically the Bi-Conjugate Gradient Method (Bi-CG) (Fletcher, Conjugate gradient methods for indefinite systems. In: Proceedings of the Dundee conference on numerical analysis, pp 73–89, 1976), restarted Generalized Minimal Residual (GMRES(m)) (Saad and Schultz, SIAM J Sci Stat Comput 7:856–869, 1986), and Bi-Conjugate Gradient Stabilized method (Bi-CGSTAB) (van der Vorst, SIAM J Sci Stat Comput 13(2):631–644, 1992).

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BT - Numerical Mathematics and Advanced Applications ENUMATH 2015

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PB - Springer

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ER -

Astudillo Rengifo R, van Gijzen M. The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems. In Karasözen B, Manguoğlu M, Tezer-Sezgin M, Göktepe S, Uğur Ö, editors, Numerical Mathematics and Advanced Applications ENUMATH 2015. Springer. 2016. p. 295-303. (Lecture Notes in Computational Science and Engineering). doi: 10.1007/978-3-319-39929-4_29

The Induced Dimension Reduction Method Applied to Convection-Diffusion-Reaction Problems

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