A novel robust strategy for discontinuous Galerkin methods in computational fluid mechanics: Why? When? What? Where?
GJ Gassner, AR Winters - Frontiers in Physics, 2021 - frontiersin.org
In this paper we will review a recent emerging paradigm shift in the construction and
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …
analysis of high order Discontinuous Galerkin methods applied to approximate solutions of …
Model order reduction via moment-matching: a state of the art review
D Rafiq, MA Bazaz - Archives of Computational Methods in Engineering, 2022 - Springer
The past few decades have seen a significant spurt in developing lower-order, parsimonious
models of large-scale dynamical systems used for design and control. These surrogate …
models of large-scale dynamical systems used for design and control. These surrogate …
Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes
This work focuses on the conservation of quantities such as Hamiltonians, mass, and
momentum when solution fields of partial differential equations are approximated with …
momentum when solution fields of partial differential equations are approximated with …
Canonical and noncanonical Hamiltonian operator inference
A method for the nonintrusive and structure-preserving model reduction of canonical and
noncanonical Hamiltonian systems is presented. Based on the idea of operator inference …
noncanonical Hamiltonian systems is presented. Based on the idea of operator inference …
On the impact of dimensionally-consistent and physics-based inner products for POD-Galerkin and least-squares model reduction of compressible flows
Abstract Model reduction of the compressible Euler equations based on proper orthogonal
decomposition (POD) and Galerkin orthogonality or least-squares residual minimization …
decomposition (POD) and Galerkin orthogonality or least-squares residual minimization …
Registration-based model reduction of parameterized two-dimensional conservation laws
We propose a nonlinear registration-based model reduction procedure for rapid and reliable
solution of parameterized two-dimensional steady conservation laws. This class of problems …
solution of parameterized two-dimensional steady conservation laws. This class of problems …
Goal-oriented model reduction for parametrized time-dependent nonlinear partial differential equations
MK Sleeman, M Yano - Computer Methods in Applied Mechanics and …, 2022 - Elsevier
We present a projection-based model reduction formulation for parametrized time-
dependent nonlinear partial differential equations (PDEs). Our approach builds on the …
dependent nonlinear partial differential equations (PDEs). Our approach builds on the …
Full and reduced order model consistency of the nonlinearity discretization in incompressible flows
S Ingimarson, LG Rebholz, T Iliescu - Computer Methods in Applied …, 2022 - Elsevier
We investigate both theoretically and numerically the consistency between the nonlinear
discretization in full order models (FOMs) and reduced order models (ROMs) for …
discretization in full order models (FOMs) and reduced order models (ROMs) for …
Efficient hyperreduction of high-order discontinuous Galerkin methods: element-wise and point-wise reduced quadrature formulations
E Du, M Yano - Journal of Computational Physics, 2022 - Elsevier
We develop and assess projection-based model reduction methods for high-order
discontinuous Galerkin (DG) discretizations of parametrized nonlinear partial differential …
discontinuous Galerkin (DG) discretizations of parametrized nonlinear partial differential …
Entropy stable modal discontinuous Galerkin schemes and wall boundary conditions for the compressible Navier-Stokes equations
Entropy stable schemes ensure that physically meaningful numerical solutions also satisfy a
semi-discrete entropy inequality under appropriate boundary conditions. In this work, we …
semi-discrete entropy inequality under appropriate boundary conditions. In this work, we …