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Separated response surfaces for flows in parametrised domains: Comparison of a priori and a posteriori PGD algorithms
Finite Elements in Analysis and Design, Volume: 196, Start page: 103530
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Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comp...
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Reduced order models (ROM) are commonly employed to solve parametric problems and to devise inexpensive response surfaces to evaluate quantities of interest in real-time. There are many families of ROMs in the literature and choosing among them is not always a trivial task. This work presents a comparison of the performance of a priori and a posteriori proper generalised decomposition (PGD) algorithms for an incompressible Stokes flow problem in a geometrically parametrised domain. This problem is particularly challenging as the geometric parameters affect both the solution manifold and the computational spatial domain. The difficulty is further increased because multiple geometric parameters are considered and extended ranges of values are analysed for the parameters and this leads to significant variations in the flow features. Using a set of numerical experiments involving geometrically parametrised microswimmers, the two PGD algorithms are extensively compared in terms of their accuracy and their computational cost, expressed as a function of the number of full-order solves required.
Reduced order models, A priori, A posteriori, Proper generalised decomposition, Response surfaces, Geometry parametrisation
College of Engineering
This work was partially supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Actions (Grant number: 675919) that financed the Ph.D. fellowship of L.B. and by the Spanish Ministry of Economy and Competitiveness (Grant number: DPI2017-85139-C2-2-R). M.G. and A.H. are also grateful for the support provided by the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa programme for centres of excellence in RTD (Grant number: CEX2018-000797-S) and the Generalitat de Catalunya (Grant number: 2017-SGR-1278). R.S. also acknowledges the support of the Engineering and Physical Sciences Research Council (Grant number: EP/P033997/1).