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

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

doi:10.1002/nme.5453

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

Journal Article · Wed Oct 26 00:00:00 EDT 2016 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5453· OSTI ID:1533197

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

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

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. Finally, various numerical results indicate the efficacy of the approach.

View Accepted Manuscript (DOE)

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

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0009279; SC0009324

OSTI ID:: 1533197

Alternate ID(s):: OSTI ID: 1401881

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 2 Vol. 111; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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

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

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References (28)

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