The sparse-grid combination technique applied to time-dependent advection problems

B. Lastdrager; B. Koren; J.G. Verwer

The sparse-grid combination technique applied to time-dependent advection problems

B. Lastdrager, B. Koren, J.G. Verwer

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence of a single, fine uniform grid. We present error estimates for the two-dimensional, spatially constant-coefficient model problem and discuss numerical examples. A spatially variable-coefficient problem (Molenkamp-Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp-Crowley test standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.

Original language	English
Title of host publication	Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999)
Editors	E. Dick, K. Riemslagh, J. Vierendeels
Place of Publication	Berlin
Publisher	Springer
Pages	143-149
ISBN (Print)	3-540-67157-9
Publication status	Published - 2000

Publication series

Name	Lecture Notes in Computational Science and Engineering
Volume	14
ISSN (Print)	1439-7358

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Lastdrager, B., Koren, B., & Verwer, J. G. (2000). The sparse-grid combination technique applied to time-dependent advection problems. In E. Dick, K. Riemslagh, & J. Vierendeels (Eds.), Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999) (pp. 143-149). (Lecture Notes in Computational Science and Engineering; Vol. 14). Springer.

Lastdrager, B. ; Koren, B. ; Verwer, J.G. / The sparse-grid combination technique applied to time-dependent advection problems. Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999). editor / E. Dick ; K. Riemslagh ; J. Vierendeels. Berlin : Springer, 2000. pp. 143-149 (Lecture Notes in Computational Science and Engineering).

@inproceedings{91add111395d48d18233ebf56cd70620,

title = "The sparse-grid combination technique applied to time-dependent advection problems",

abstract = "In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence of a single, fine uniform grid. We present error estimates for the two-dimensional, spatially constant-coefficient model problem and discuss numerical examples. A spatially variable-coefficient problem (Molenkamp-Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp-Crowley test standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.",

author = "B. Lastdrager and B. Koren and J.G. Verwer",

year = "2000",

language = "English",

isbn = "3-540-67157-9",

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

publisher = "Springer",

pages = "143--149",

editor = "E. Dick and K. Riemslagh and J. Vierendeels",

booktitle = "Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999)",

address = "Germany",

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Lastdrager, B, Koren, B & Verwer, JG 2000, The sparse-grid combination technique applied to time-dependent advection problems. in E Dick, K Riemslagh & J Vierendeels (eds), Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999). Lecture Notes in Computational Science and Engineering, vol. 14, Springer, Berlin, pp. 143-149.

The sparse-grid combination technique applied to time-dependent advection problems. / Lastdrager, B.; Koren, B.; Verwer, J.G.

Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999). ed. / E. Dick; K. Riemslagh; J. Vierendeels. Berlin : Springer, 2000. p. 143-149 (Lecture Notes in Computational Science and Engineering; Vol. 14).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

TY - GEN

T1 - The sparse-grid combination technique applied to time-dependent advection problems

AU - Lastdrager, B.

AU - Koren, B.

AU - Verwer, J.G.

PY - 2000

Y1 - 2000

N2 - In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence of a single, fine uniform grid. We present error estimates for the two-dimensional, spatially constant-coefficient model problem and discuss numerical examples. A spatially variable-coefficient problem (Molenkamp-Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp-Crowley test standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.

AB - In the numerical technique considered in this paper, time-stepping is performed on a set of semi-coarsened space grids. At given time levels the solutions on the different space grids are combined to obtain the asymptotic convergence of a single, fine uniform grid. We present error estimates for the two-dimensional, spatially constant-coefficient model problem and discuss numerical examples. A spatially variable-coefficient problem (Molenkamp-Crowley test) is used to assess the practical merits of the technique. The combination technique is shown to be more efficient than the single-grid approach, yet for the Molenkamp-Crowley test standard Richardson extrapolation is still more efficient than the combination technique. However, parallelization is expected to significantly improve the combination technique's performance.

M3 - Conference contribution

SN - 3-540-67157-9

T3 - Lecture Notes in Computational Science and Engineering

SP - 143

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BT - Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999)

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A2 - Riemslagh, K.

A2 - Vierendeels, J.

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Lastdrager B, Koren B, Verwer JG. The sparse-grid combination technique applied to time-dependent advection problems. In Dick E, Riemslagh K, Vierendeels J, editors, Multigrid Methods VI (Proceedings of the Sixth European Multigrid Conference, Gent, Belgium, September 27-30, 1999). Berlin: Springer. 2000. p. 143-149. (Lecture Notes in Computational Science and Engineering).