least-squares Petrov--Galerkin projection

Space–time least-squares Petrov–Galerkin projection for nonlinear model reduction

This work proposes a space--time least-squares Petrov--Galerkin (ST-LSPG) projection method for model reduction of nonlinear dynamical systems. In contrast to typical nonlinear model-reduction methods that first apply (Petrov--)Galerkin projection …

Accelerated solution of discrete ordinates approximation to the Boltzmann transport equation via model reduction

Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, …

The GNAT method for nonlinear model reduction: Effective implementation and application to computational fluid dynamics and turbulent flows

The Gauss–Newton with approximated tensors (GNAT) method is a nonlinear model-reduction method that operates on fully discretized computational models. It achieves dimension reduction by a Petrov--Galerkin projection associated with residual …

The GNAT nonlinear model reduction method and its application to fluid dynamics problems

The goal of this work is to accurately evaluate large-scale, nonlinear, finite-volume-based fluid dynamics models at low computational cost. To accomplish this objective, this work employs the Gauss– Newton with approximated tensors (GNAT) nonlinear …

Efficient non-linear model reduction via a least-squares Petrov–Galerkin projection and compressive tensor approximations

A Petrov--Galerkin projection method is proposed for reducing the dimension of a discrete non‐linear static or dynamic computational model in view of enabling its processing in real time. The right reduced‐order basis is chosen to be invariant and is …

Reduced order modeling applied to the discrete ordinates method for radiation heat transfer in participating media

Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, …