A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Yalchin R. Efendiev; Raytcho D. Lazarov; Minam Moon; Ke Shi

doi:10.1016/j.cma.2014.09.036

A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Yalchin R. Efendiev, Raytcho D. Lazarov, Minam Moon, Ke Shi

Computer, Electrical and Mathematical Sciences and Engineering

Research output: Contribution to journal › Article › peer-review

31 Scopus citations

Abstract

We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

Original language	English (US)
Pages (from-to)	243-256
Number of pages	14
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	292
DOIs	https://doi.org/10.1016/j.cma.2014.09.036
State	Published - Oct 22 2014

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: YE's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project. R. Lazarov's research was supported in part by the National Science Foundation (DMS-1016525).

ASJC Scopus subject areas

General Physics and Astronomy
Mechanics of Materials
Mechanical Engineering
Computational Mechanics
Computer Science Applications

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10.1016/j.cma.2014.09.036

https://repository.kaust.edu.sa/bitstream/10754/566068/1/Articlefile1.pdf

Cite this

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title = "A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems",

abstract = "We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.",

author = "Efendiev, {Yalchin R.} and Lazarov, {Raytcho D.} and Minam Moon and Ke Shi",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: YE's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project. R. Lazarov's research was supported in part by the National Science Foundation (DMS-1016525).",

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AU - Efendiev, Yalchin R.

AU - Lazarov, Raytcho D.

AU - Moon, Minam

AU - Shi, Ke

N1 - KAUST Repository Item: Exported on 2020-10-01 Acknowledgements: YE's work is partially supported by the U.S. Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-FG02-13ER26165, and the DoD Army ARO Project. R. Lazarov's research was supported in part by the National Science Foundation (DMS-1016525).

PY - 2014/10/22

Y1 - 2014/10/22

N2 - We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

AB - We design a multiscale model reduction framework within the hybridizable discontinuous Galerkin finite element method. Our approach uses local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We propose several multiscale finite element spaces on the coarse edges that provide a reduced dimensional approximation for numerical traces within the HDG framework. We provide a general framework for systematic construction of multiscale trace spaces. Using local snapshots, we avoid high dimensional representation of trace spaces and use some local features of the solution space in constructing a low dimensional trace space. We investigate the solvability and numerically study the performance of the proposed method on a representative number of numerical examples.

UR - http://hdl.handle.net/10754/566068

UR - https://manuscript.elsevier.com/S0045782514003594/pdf/S0045782514003594.pdf

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DO - 10.1016/j.cma.2014.09.036

M3 - Article

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SP - 243

EP - 256

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

ER -

A spectral multiscale hybridizable discontinuous Galerkin method for second order elliptic problems

Abstract

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ASJC Scopus subject areas

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