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Parameterized Non-intrusive Reduced Order Model And Error Analysis For General Time-dependent Nonlinear Partial Differential Equations And Its Applications

Title: A Parameterized Non-intrusive Reduced Order Model And Error Analysis For General Time-dependent Nonlinear Partial Differential Equations And Its Applications.
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Name(s): Xiao, D., author
Fang, F., author
Pain, C. C., author
Navon, I. M., author
Type of Resource: text
Genre: Journal Article
Text
Journal Article
Date Issued: 2017-04-15
Physical Form: computer
online resource
Extent: 1 online resource
Language(s): English
Abstract/Description: A novel parameterized non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) has been developed. This P-NIROM is a generic and efficient approach for model reduction of parameterized partial differential equations (P-PDEs). Over existing parameterized reduced order models (P-ROM) (most of them are based on the reduced basis method), it is non-intrusive and independent on partial differential equations and computational codes. During the training process, the Smolyak sparse grid method is used to select a set of parameters over a specific parameterized space (ohm(p) is an element of R-P). For each selected parameter, the reduced basis functions are generated from the snapshots derived from a run of the high fidelity model. More generally, the snapshots and basis function sets for any parameters over Op can be obtained using an interpolation method. The P-NIROM can then be constructed by using our recently developed technique (Xiao et al., 2015 [ 41,42]) where either the Smolyak or radial basis function (RBF) methods are used to generate a set of hyper-surfaces representing the underlying dynamical system over the reduced space. The new P-NIROM technique has been applied to parameterized Navier-Stokes equations and implemented with an unstructured mesh finite element model. The capability of this P-NIROM has been illustrated numerically by two test cases: flow past a cylinder and lock exchange case. The prediction capabilities of the P-NIROM have been evaluated by varying the viscosity, initial and boundary conditions. The results show that this P-NIROM has captured the quasi-totality of the details of the flow with CPU speedup of three orders of magnitude. An error analysis for the P-NIROM has been carried out. (C) 2016 Elsevier B.V. All rights reserved.
Identifier: FSU_libsubv1_wos_000398373500035 (IID), 10.1016/j.cma.2016.12.033 (DOI)
Keywords: empirical interpolation, finite-element methods, fluid-flow, Non-intrusive ROM, Parameterized, pde, petrov-galerkin methods, pod, proper orthogonal decomposition, rbf, reduction, shallow-water equations, Smolyak sparse grid, sparse grids, strategies, variational data assimilation
Publication Note: The publisher's version of record is available at https://doi.org/10.1016/j.cma.2016.12.033
Persistent Link to This Record: http://purl.flvc.org/fsu/fd/FSU_libsubv1_wos_000398373500035
Owner Institution: FSU
Is Part Of: Computer Methods in Applied Mechanics and Engineering.
0045-7825
Issue: vol. 317

Choose the citation style.
Xiao, D., Fang, F., Pain, C. C., & Navon, I. M. (2017). A Parameterized Non-intrusive Reduced Order Model And Error Analysis For General Time-dependent Nonlinear Partial Differential Equations And Its Applications. Computer Methods In Applied Mechanics And Engineering. Retrieved from http://purl.flvc.org/fsu/fd/FSU_libsubv1_wos_000398373500035