Related papers: Stability-preserving model order reduction for lin…
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…
We investigate linear dynamical systems of second order. Uncertainty quantification is applied, where physical parameters are substituted by random variables. A stochastic Galerkin method yields a linear dynamical system of second order…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to…
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equations. The unknown solution is expanded into an orthogonal…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear dynamical system with many linear outputs. MOR is feasible…
We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimensions. However, a reduced system may be unstable, although…
We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodelled as random variables to conduct an uncertainty quantification. A stochastic Galerkin…
Projection-based nonlinear model order reduction methods can be used to reduce simulation times for the solution of many PDE-constrained problems. It has been observed in literature that such nonlinear reduced-order models (ROMs) based on…
We investigate model order reduction (MOR) strategies for simulating unsteady hemodynamics within cerebrovascular systems, contrasting a physics-based intrusive approach with a data-driven non-intrusive framework. High-fidelity 3D…
Systems of differential-algebraic equations (DAEs) represent a widespread formalism in the modeling of constrained mechanical systems and electrical networks. Due to the automatic, object-oriented generation of the equations of motion and…
This paper considers structure-preserving model order reduction (MOR) techniques for port-Hamiltonian (pH) systems, which are typically derived from energy-based modelling. To keep favorable properties of pH systems such as stability and…
Here, we focus on Model Order Reduction (MOR) of non-parametric second-order dynamical systems. In these MOR algorithms, sequences of large and sparse linear systems arise during the model reduction process. Solving such linear systems is…
We present a method for linear stability analysis of systems with parametric uncertainty formulated in the stochastic Galerkin framework. Specifically, we assume that for a model partial differential equation, the parameter is given in the…
We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…
In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…
We consider linear dynamical systems of ordinary differential equations or differential algebraic equations. Physical parameters are substituted by random variables for an uncertainty quantification. We expand the state variables as well as…
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…
The purpose of this work is to present a reduced order modeling framework for parametrized turbulent flows with moderately high Reynolds numbers within the variational multiscale (VMS) method. The Reduced Order Models (ROMs) presented in…