<abstract xmlns="http://www.w3.org/1999/xhtml"><p>This paper addresses the issue of offline and online computational cost reduction of the proper orthogonal decomposition (POD) which is a popular nonlinear model order reduction (MOR) technique. Online computational cost is reduced by using the discrete empirical interpolation method (DEIM), which reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD: this is the POD-DEIM approach. Offline computational cost is reduced by generating an approximate snapshot-ensemble of the nonlinear dynamical system, consequently, completely avoiding the need to simulate the full-order system. Two snapshot ensembles: one of the states and the other of the nonlinear function are obtained by simulating the successive linearization of the original nonlinear system. The proposed technique is applied to two benchmark large-scale nonlinear dynamical systems and clearly demonstrates comprehensive savings in computational cost and time with insignificant or no deterioration in performance.</p></abstract>

This paper addresses the issue of offline and online computational cost reduction of the proper orthogonal decomposition (POD) which is a popular nonlinear model order reduction (MOR) technique. Online computational cost is reduced by using the discrete empirical interpolation method (DEIM), which reduces the complexity of evaluating the nonlinear term of the reduced model to a cost proportional to the number of reduced variables obtained by POD: this is the POD-DEIM approach. Offline computational cost is reduced by generating an approximate snapshot-ensemble of the nonlinear dynamical system, consequently, completely avoiding the need to simulate the full-order system. Two snapshot ensembles: one of the states and the other of the nonlinear function are obtained by simulating the successive linearization of the original nonlinear system. The proposed technique is applied to two benchmark large-scale nonlinear dynamical systems and clearly demonstrates comprehensive savings in computational cost and time with insignificant or no deterioration in performance.

A scheme for comprehensive computational cost reduction in proper orthogonal decomposition

Department. of Electrical Engineering, National Institute of Technology

Journal of Electrical Engineering

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

This paper addresses the issue of offline and online computational cost reduction of the proper orthogonal decomposition (POD) which is a popular nonlinear...

A scheme for comprehensive computational cost reduction in proper orthogonal decomposition

Published Online: Sep 19, 2018

Page range: 279 - 285

Received: Jul 30, 2018

DOI: https://doi.org/10.2478/jee-2018-0039

Keywords
proper orthogonal decomposition, reduced order model, discrete empirical interpolation, approximate snapshot ensemble

© 2018 Satyavir Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

A scheme for comprehensive computational cost reduction in proper orthogonal decomposition

Published Online: Sep 19, 2018

Page range: 279 - 285

Received: Jul 30, 2018

DOI: https://doi.org/10.2478/jee-2018-0039

Keywordsproper orthogonal decomposition, reduced order model, discrete empirical interpolation, approximate snapshot ensemble

© 2018 Satyavir Singh et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
proper orthogonal decomposition, reduced order model, discrete empirical interpolation, approximate snapshot ensemble