4 citations · 7 across the 10 of their papers we have counts for
17 papers
Stochastic Galerkin method and port-Hamiltonian form for linear first-order ordinary differential equations
Roland Pulch, Olivier Sète
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…
Energy-based model order reduction for linear stochastic Galerkin systems of second order
Roland Pulch
We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear sys…
Stochastic Galerkin method and port-Hamiltonian form for linear dynamical systems of second order
Roland Pulch
We investigate linear dynamical systems of second order. Uncertainty quantification is applied, where physical parameters are substituted by random variables. A stochastic Galerkin…
The Helmholtz equation with uncertainties in the wavenumber
Roland Pulch, Olivier Sète
We investigate the Helmholtz equation with suitable boundary conditions and uncertainties in the wavenumber. Thus the wavenumber is modeled as a random variable or a random field.…
Machine Learning for Initial Value Problems of Parameter-Dependent Dynamical Systems
Roland Pulch, Maha Youssef
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation…
Stability-preserving model order reduction for linear stochastic Galerkin systems
Roland Pulch
Mathematical modeling often yields linear dynamical systems in science and engineering. We change physical parameters of the system into random variables to perform an uncertainty…
Poly-Sinc Solution of Stochastic Elliptic Differential Equations
Maha Youssef, Roland Pulch
In this paper, we introduce a numerical solution of a stochastic partial differential equation (SPDE) of elliptic type using polynomial chaos along side with polynomial approximati…
Sensitivity analysis of random linear dynamical systems using quadratic outputs
Roland Pulch, Akil Narayan
In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary di…
Time and Frequency Domain Methods for Basis Selection in Random Linear Dynamical Systems
John D. Jakeman, Roland Pulch
Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approxima…
Sparse Representations for Uncertainty Quantification of a Coupled Field-Circuit Problem
Roland Pulch, Sebastian Schöps
We consider a model of an electric circuit, where differential algebraic equations for a circuit part are coupled to partial differential equations for an electromagnetic field par…
Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction
Roland Pulch
We investigate linear dynamical systems consisting of ordinary differential equations with high dimensionality. Model order reduction yields alternative systems of much lower dimen…
Stability preservation in Galerkin-type projection-based model order reduction
Roland Pulch
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating syste…
Balanced truncation for model order reduction of linear dynamical systems with quadratic outputs
Roland Pulch, Akil Narayan
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…
Stability preservation in stochastic Galerkin projections of dynamical systems
Roland Pulch, Florian Augustin
In uncertainty quantification, critical parameters of mathematical models are substituted by random variables. We consider dynamical systems composed of ordinary differential equat…
Index-analysis for a method of lines discretising multirate partial differential algebraic equations
Roland Pulch, Diana Estevez Schwarz, Rene Lamour
In radio frequency applications, electric circuits generate signals, which are amplitude modulated and/or frequency modulated. A mathematical modelling yields typically systems of…
Model order reduction for random nonlinear dynamical systems and low-dimensional representations for their quantities of interest
Roland Pulch
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by…
Model order reduction and sparse orthogonal expansions for random linear dynamical systems
Roland Pulch
We consider linear dynamical systems of ordinary differential equations or differential algebraic equations. Physical parameters are substituted by random variables for an uncertai…