University of Twente Student Theses


Reduced-order surrogate modeling for linear-nonlinear coupled problems

Stuiver, Paul (2023) Reduced-order surrogate modeling for linear-nonlinear coupled problems.

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Abstract:Introduction: Parametrized linear-nonlinear coupled problems consist of a linear and non-linear sub-domain that are coupled via a non-overlapping interface. Solving these problems with a conventional full-order approach such as the finite element method (FEM) is usually paired with prohibitive computational cost. Reduced-order models are required to address these limitations. Methods: We developed reduced-order surrogate models to solve parametrized linear-nonlinear coupled problems with improved efficiency. These models utilize domain decomposition to apply both intrusive and non-intrusive reduced-order methods with POD-ROM and POD-NN on sub-domains separately. The choices of the reduction techniques on the sub-domains are based on the parametric complexity and the underlying equations (linear or non-linear) in order to implement reduction effectively. The designed ROMs termed hybrid-LL and surrogate-LL act as proof of concepts to solve linear-linear coupled problems, while the hybrid-NL and surrogate-NL are designed to solve linear-nonlinear coupled problems. Results: We report the performance of the ROMs on three steady-state PDEs with increased parametric complexity. While both the hybrid-NL and surrogate-NL guarantee solutions, the hybrid-NL is inaccurate for particular parameter locations and is usually costly. In contrast, the surrogate-NL is successfully tested and shows minimal errors with extremely low computational costs. Equally, in the field of uncertainty quantification, the surrogate-NL shows promising results using Monte Carlo simula- tions. Conclusion: While the hybrid-NL does not perform as desired due to lacking robustness and computational gain, the surrogate-NL has shown to perform remarkably well with low errors and computational cost.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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