Related papers: Parametric POD-Galerkin Model Order Reduction for …
We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this…
The inviscid, partial differential equations of hydrodynamics when projected via a Galerkin-truncation on a finite-dimensional subspace spanning wavenumbers $-{\bf K}_{\rm G} \le {\bf k} \le {\bf K}_{\rm G}$, and hence retaining a finite…
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when…
Coexisting fluctuations towards various ordered states are ubiquitous in strongly correlated electronic systems. In particular, measurements of underdoped cuprate high-temperature superconductors reveal evidence for short range charge order…
In this paper, a type of novel projection-based, time-segmented reduced order model (ROM) is proposed for dynamic fluid-structure interaction (FSI) problems based upon the arbitrary Lagrangian--Eulerian (ALE)-finite element method (FEM) in…
In the context of Galerkin discretizations of a partial differential equation (PDE), the modes of the classical method of Proper Orthogonal Decomposition (POD) can be interpreted as the ansatz and trial functions of a low-dimensional…
In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…
In this paper, we develop a sparse grid discontinuous Galerkin (DG) scheme for transport equations and applied it to kinetic simulations. The method uses the weak formulations of traditional Runge-Kutta DG (RKDG) schemes for hyperbolic…
In this chapter we introduce a combined parameter and model reduction methodology and present its application to the efficient numerical estimation of a pressure drop in a set of deformed carotids. The aim is to simulate a wide range of…
An energy preserving reduced order model is developed for two dimensional nonlinear Schr\"odinger equation (NLSE) with plane wave solutions and with an external potential. The NLSE is discretized in space by the symmetric interior penalty…
Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…
Projection-based Reduced Order Models minimize the discrete residual of a "full order model" (FOM) while constraining the unknowns to a reduced dimension space. For problems with symmetric positive definite (SPD) Jacobians, this is…
In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…
We present a general framework for studying strongly coupled radiative and conductive heat transfer between arbitrarily shaped bodies separated by sub-wavelength distances. Our formulation is based on a macroscopic approach that couples our…
We explore a reduced-order model (ROM) of plane Couette flow with a view to performing turbulence control. The ROM is derived through Galerkin projections of the incompressible Navier-Stokes (NS) system onto a basis composed of…
A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…
In this contribution, we coupled the isogeometric analysis to a reduced order modelling technique in order to provide a computationally efficient solution in parametric domains. In details, we adopt the free-form deformation method to…
Plasmas are highly nonlinear and multi-scale, motivating a hierarchy of models to understand and describe their behavior. However, there is a scarcity of plasma models of lower fidelity than magnetohydrodynamics (MHD), although these…
We discuss a multiscale Galerkin approximation scheme for a system of coupled quasilinear parabolic equations. These equations arise from the upscaling of a pore scale filtration combustion model under the assumptions of large Damkh\"oler…
We introduce optimization-based full-order and reduced-order formulations of fluid structure interaction problems. We study the flow of an incompressible Newtonian fluid which interacts with an elastic body: we consider an arbitrary…