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Model order reduction of nonlinear parabolic PDE systems with moving boundaries using sparse proper orthogonal decomposition methodology | IEEE Conference Publication | IEEE Xplore

Model order reduction of nonlinear parabolic PDE systems with moving boundaries using sparse proper orthogonal decomposition methodology


Abstract:

Developing reduced-order models for nonlinear parabolic partial differential equation (PDE) systems with time-varying spatial domains remains a key challenge as the domin...Show More

Abstract:

Developing reduced-order models for nonlinear parabolic partial differential equation (PDE) systems with time-varying spatial domains remains a key challenge as the dominant spatial patterns of the system change with time. Within this context, there have been several studies where the time-varying spatial domain is transformed to the time-invariant spatial domain by using an analytical expression that describes how the spatial domain changes with time. However, this information is not available in many real-world applications and therefore, the approach is not generally applicable. To overcome this challenge, we introduce sparse proper orthogonal decomposition (SPOD)-Galerkin methodology that exploits the key features of ridge and lasso regularization techniques for the model order reduction of such systems. This methodology is successfully applied to a hydraulic fracturing process, and a series of simulation results indicates that it is more accurate in approximating the original nonlinear system than the standard POD-Galerkin methodology.
Date of Conference: 27-29 June 2018
Date Added to IEEE Xplore: 16 August 2018
ISBN Information:
Electronic ISSN: 2378-5861
Conference Location: Milwaukee, WI, USA

References

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