Exploration of efficient reduced-order modeling and a posteriori error estimation

Chaudhry, J. H.; Estep, D.; Gunzburger, M.

doi:10.1002/nme.5453

Title: Exploration of efficient reduced-order modeling and a posteriori error estimation

Abstract

Summary Efficient algorithms are considered for the computation of a reduced‐order model based on the proper orthogonal decomposition methodology for the solution of parameterized elliptic partial differential equations. The method relies on partitioning the parameter space into subdomains based on the properties of the solution space and then forming a reduced basis for each of the subdomains. This yields more efficient offline and online stages for the proper orthogonal decomposition method. We extend these ideas for inexpensive adjoint based a posteriori error estimation of both the expensive finite element method solutions and the reduced‐order model solutions, for a single and multiple quantities of interest. Various numerical results indicate the efficacy of the approach. Copyright © 2016 John Wiley & Sons, Ltd.

Authors:

Chaudhry, J. H. ^[1]; Estep, D. ^[2]; Gunzburger, M. ^[3]

Univ. of New Mexico, Albuquerque, NM (United States)
Colorado State Univ., Fort Collins, CO (United States)
Florida State Univ., Tallahassee, FL (United States)

Publication Date:: Wed Oct 26 00:00:00 EDT 2016

Research Org.:: Colorado State Univ., Fort Collins, CO (United States); Florida State Univ., Tallahassee, FL (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1533197

Alternate Identifier(s):: OSTI ID: 1401881

Grant/Contract Number:: SC0009279; SC0009324

Resource Type:: Accepted Manuscript

Journal Name:: International Journal for Numerical Methods in Engineering

Additional Journal Information:: Journal Volume: 111; Journal Issue: 2; Journal ID: ISSN 0029-5981

Publisher:: Wiley

Country of Publication:: United States

Language:: English

Subject:: 42 ENGINEERING; engineering; mathematics; error estimation; reduced-order modeling; a posteriori analysis; quantity of interest; proper orthogonal decomposition

Citation Formats


                    Chaudhry, J. H., Estep, D., and Gunzburger, M. Exploration of efficient reduced-order modeling and a posteriori error estimation.  United States: N. p., 2016. 
Web.  doi:10.1002/nme.5453.

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                    Chaudhry, J. H., Estep, D., & Gunzburger, M. Exploration of efficient reduced-order modeling and a posteriori error estimation.  United States.  https://doi.org/10.1002/nme.5453

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                    Chaudhry, J. H., Estep, D., and Gunzburger, M. Wed .  
"Exploration of efficient reduced-order modeling and a posteriori error estimation".  United States.  https://doi.org/10.1002/nme.5453.  https://www.osti.gov/servlets/purl/1533197.

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@article{osti_1533197,

  title        = {Exploration of efficient reduced-order modeling and a posteriori error estimation},

  author       = {Chaudhry, J. H. and Estep, D. and Gunzburger, M.},

  abstractNote = {Summary Efficient algorithms are considered for the computation of a reduced‐order model based on the proper orthogonal decomposition methodology for the solution of parameterized elliptic partial differential equations. The method relies on partitioning the parameter space into subdomains based on the properties of the solution space and then forming a reduced basis for each of the subdomains. This yields more efficient offline and online stages for the proper orthogonal decomposition method. We extend these ideas for inexpensive adjoint based a posteriori error estimation of both the expensive finite element method solutions and the reduced‐order model solutions, for a single and multiple quantities of interest. Various numerical results indicate the efficacy of the approach. Copyright © 2016 John Wiley & Sons, Ltd.},

  doi          = {10.1002/nme.5453},

  journal      = {International Journal for Numerical Methods in Engineering},

  number       = 2,

  volume       = 111,

  place        = {United States},

  year         = {Wed Oct 26 00:00:00 EDT 2016},

  month        = {Wed Oct 26 00:00:00 EDT 2016}

}

Copy to clipboard

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Works referencing / citing this record:

Enhancing piecewise‐defined surrogate response surfaces with adjoints on sets of unstructured samples to solve stochastic inverse problems
journal, May 2019

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Title: Exploration of efficient reduced-order modeling and a posteriori error estimation

Abstract

Citation Formats

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Nonlinear model order reduction based on local reduced-order bases: NONLINEAR MODEL REDUCTION BASED ON LOCAL REDUCED-ORDER BASES
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Interpolation Method for Adapting Reduced-Order Models and Application to Aeroelasticity
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Reduced Basis Technique for Nonlinear Analysis of Structures
journal, April 1980

Certified reduced basis approximation for parametrized partial differential equations and applications
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Least squares quantization in PCM
journal, March 1982

A-Posteriori Error Estimation of Discrete POD Models for PDE-Constrained Optimal Control
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Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations: Application to Transport and Continuum Mechanics
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Computational Reduction for Parametrized PDEs: Strategies and Applications
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Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data
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Reduced-order model feedback control design: numerical implementation in a thin shell model
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