Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discretize-then-map approach for the treatment of parameterized
  geometries in model order reduction   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 $\{ \Omega_{\mu}: \mu \in \mathcal{P} \}
\subset \mathbb{R}^D$ where $\mu \in \mathcal{P} \subset \mathbb{R}^P$ denotes
a vector of parameters, (ii) a parameterized mapping ${\Phi}_{\mu}$ between a
reference domain $\Omega$ and the parameter-dependent domain $\Omega_{\mu}$,
and (iii) a finite element triangulation of $\Omega$, 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.

30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio