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arXiv · 2010.13935

A discretize-then-map approach for the treatment of parameterized geometries in model order reduction

Tommaso Taddei·Lei Zhang
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Abstract

We present a general approach for the treatment of parameterized geometries in projection-based model order reduction. During the offline stage, given (i) a family of parameterized domains $\{ Ω_μ: μ\in \mathcal{P} \} \subset \mathbb{R}^D$ where $μ\in \mathcal{P} \subset \mathbb{R}^P$ denotes a vector of parameters, (ii) a parameterized mapping $Φ_μ$ between a reference domain $Ω$ and the parameter-dependent domain $Ω_μ$, and (iii) a finite element triangulation of $Ω$, we resort to an empirical quadrature procedure to select a subset of the elements of the grid. During the online stage, we first use the mapping to "move" the nodes of the selected elements and then we use standard element-wise residual evaluation routines to evaluate the residual and possibly its Jacobian. We discuss how to devise an online-efficient reduced-order model and we discuss the differences with the more standard "map-then-discretize" approach (e.g., Rozza, Huynh, Patera, ACME, 2007); in particular, we show how the discretize-then-map framework greatly simplifies the implementation of the reduced-order model. We apply our approach to a two-dimensional potential flow problem past a parameterized airfoil, and to the two-dimensional RANS simulations of the flow past the Ahmed body.

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Tommaso Taddei, Lei Zhang. 2021-03-24. A discretize-then-map approach for the treatment of parameterized geometries in model order reduction. https://doi.org/10.1016/j.cma.2021.113956

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