A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems

Mario Ohlberger; Kathrin Smetana

A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems

Mario Ohlberger, Kathrin Smetana^*

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.

Original language	English
Title of host publication	ECCOMAS Thematic Conference - ADMOS 2011
Subtitle of host publication	International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference
Pages	343-354
Number of pages	12
Publication status	Published - 16 Aug 2012
Externally published	Yes
Event	5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011 - Paris, France Duration: 6 Jun 2011 → 8 Jun 2011 Conference number: 5

Conference

Conference	5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011
Abbreviated title	ADMOS 2011
Country/Territory	France
City	Paris
Period	6/06/11 → 8/06/11

Keywords

A posteriori error estimation
Adaptive modeling
Hierarchical model reduction
Model reduction
Reduced basis methods

Cite this

@inproceedings{5a2bdf6d0d6c4c56a41323f71f346ede,

title = "A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems",

abstract = "We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.",

keywords = "A posteriori error estimation, Adaptive modeling, Hierarchical model reduction, Model reduction, Reduced basis methods",

author = "Mario Ohlberger and Kathrin Smetana",

year = "2012",

month = aug,

day = "16",

language = "English",

isbn = "9788493964030",

pages = "343--354",

booktitle = "ECCOMAS Thematic Conference - ADMOS 2011",

note = "5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011, ADMOS 2011 ; Conference date: 06-06-2011 Through 08-06-2011",

}

Ohlberger, M & Smetana, K 2012, A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems. in ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference. pp. 343-354, 5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011, Paris, France, 6/06/11.

A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems. / Ohlberger, Mario; Smetana, Kathrin.
ECCOMAS Thematic Conference - ADMOS 2011: International Conference on Adaptive Modeling and Simulation, An IACM Special Interest Conference. 2012. p. 343-354.

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

TY - GEN

T1 - A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems

AU - Ohlberger, Mario

AU - Smetana, Kathrin

N1 - Conference code: 5

PY - 2012/8/16

Y1 - 2012/8/16

N2 - We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.

AB - We extend previous work on the Hierarchical Model Reduction-Reduced Basis (HMR-RB) approach to an advection-diffusion-reaction problem. In comparison to the Boussinesq approach we do not neglect the dependency on the vertical direction but enhance the solution for the horizontal direction with appropriately chosen basis functions living on the vertical one. This is done by a combination of the frameworks of hierarchical model reduction [4] and the reduced basis methods [3]. We derive a new a posteriori error estimate and demonstrate in numerical experiments that few basis functions suffice to get good approximations.

KW - A posteriori error estimation

KW - Adaptive modeling

KW - Hierarchical model reduction

KW - Model reduction

KW - Reduced basis methods

UR - https://www.scopus.com/pages/publications/84864871424

M3 - Conference contribution

AN - SCOPUS:84864871424

SN - 9788493964030

SP - 343

EP - 354

BT - ECCOMAS Thematic Conference - ADMOS 2011

T2 - 5th International Conference on Adaptive Modeling and Simulation, ADMOS 2011

Y2 - 6 June 2011 through 8 June 2011

ER -

A new hierarchical model reduction-reduced basis technique for advection-diffusion-reaction problems

Abstract

Conference

Keywords

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