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, …
Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most …
This work presents a method to adaptively refine reduced‐order models *a posteriori* without requiring additional full‐order‐model solves. The technique is analogous to mesh‐adaptive $h$‐refinement: it enriches the reduced‐basis space online by …
This work presents a method to adaptively refine reduced‐order models *a posteriori* without requiring additional full‐order‐model solves. The technique is analogous to mesh‐adaptive $h$‐refinement: it enriches the reduced‐basis space online by …
This work proposes a model-reduction methodology that preserves Lagrangian structure and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence. As such, the resulting reduced-order model …
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive 'error indicators' to a …
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 …
This work proposes a model-reduction methodology that both preserves Lagrangian structure and leads to computationally inexpensive models, even in the presence of high-order nonlinearities. We focus on parameterized simple mechanical systems under …
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 …
A novel model reduction technique for static systems is presented. The method is developed using a goal‐oriented framework, and it extends the concept of snapshots for proper orthogonal decomposition (POD) to include (sensitivity) derivatives of the …