Abstract
We propose a new model order reduction (MOR) approach to obtain effective reduction for transport-dominated problems or hyperbolic partial differential equations. The main ingredient is a novel decomposition of the solution into a function that tracks the evolving discontinuity and a residual part that is devoid of shock features. This decomposition ansatz is then combined with Proper Orthogonal Decomposition applied to the residual part only to develop an efficient reduced-order model representation for problems with multiple moving and possibly merging discontinuous features. Numerical case-studies show the potential of the approach in terms of computational accuracy compared with standard MOR techniques.
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Acknowledgements
The first author has been funded by the Shell NWO/ FOM PhD Programme in Computational Sciences for Energy Research. The second author has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044–390685587, Mathematics Muenster: Dynamics–Geometry–Structure. The authors are also grateful for the support of COST Action TD1307, EU-MORNET (www.eu-mor.net).
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Bansal, H., Rave, S., Iapichino, L., Schilders, W., Wouw, N.v.d. (2021). Model Order Reduction Framework for Problems with Moving Discontinuities. In: Vermolen, F.J., Vuik, C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham. https://doi.org/10.1007/978-3-030-55874-1_7
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