  The energy-conserving sampling and weighting (ECSW) method is a
hyperreduction method originally developed for accelerating the performance of
Galerkin projection-based reduced-order models (PROMs) associated with
large-scale finite element models, when the underlying projected operators need
to be frequently recomputed as in parametric and/or nonlinear problems. In this
paper, this hyperreduction method is extended to Petrov-Galerkin PROMs where
the underlying high-dimensional models can be associated with arbitrary finite
element, finite volume, and finite difference semi-discretization methods. Its
scope is also extended to cover local PROMs based on piecewise-affine
approximation subspaces, such as those designed for mitigating the Kolmogorov
$n$-width barrier issue associated with convection-dominated flow problems. The
resulting ECSW method is shown in this paper to be robust and accurate. In
particular, its offline phase is shown to be fast and parallelizable, and the
potential of its online phase for large-scale applications of industrial
relevance is demonstrated for turbulent flow problems with $O(10^7)$ and
$O(10^8)$ degrees of freedom. For such problems, the online part of the ECSW
method proposed in this paper for Petrov-Galerkin PROMs is shown to enable
wall-clock time and CPU time speedup factors of several orders of magnitude
while delivering exceptional accuracy.
