Exploration of efficient reduced‐order modeling and a posteriori error estimation. (16th January 2017)

• Record Type: Journal Article
• Authors: Chaudhry, J.H.; Estep, D.; Gunzburger, M.
• Is Part Of: International journal for numerical methods in engineering. Volume 111:Number 2(2017)
• Page Start: 103
• Page End: 122
• Publication Date: 2017-01-16
• Subjects: Error estimation -- reduced‐order modeling -- a posteriori analysis -- quantity of interest -- proper orthogonal decomposition; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5453
• Languages: English
• ISSNs: 0029-5981

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.