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We study the numerical approximation by space-time finite element methods of a multi-physics system coupling hyperbolic elastodynamics with parabolic transport and modeling poro- and thermoelasticity. The equations are rewritten as a…

Numerical Analysis · Mathematics 2023-02-14 Markus Bause , Mathias Anselmann , Uwe Köcher , Florin A. Radu

In this work, we analyze Parametrized Advection-Dominated distributed Optimal Control Problems with random inputs in a Reduced Order Model (ROM) context. All the simulations are initially based on a finite element method (FEM)…

Numerical Analysis · Mathematics 2024-08-27 Fabio Zoccolan , Maria Strazzullo , Gianluigi Rozza

Discontinuous Galerkin methods of higher order are applied as temporal discretizations for the transient Navier--Stokes equations. The spatial discretization based on inf-sup stable pairs of finite element spaces is stabilised using a…

Numerical Analysis · Mathematics 2019-10-29 Naveed Ahmed , Gunar Matthies

The proper orthogonal decomposition reduced-order models (POD-ROMs) have been widely used as a computationally efficient surrogate models in large-scale numerical simulations of complex systems. However, when it is applied to a Hamiltonian…

Numerical Analysis · Mathematics 2017-03-08 Yuezheng Gong , Qi Wang , Zhu Wang

Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…

Dynamical Systems · Mathematics 2026-03-19 Akira Saito , Masato Tanaka

In this note we shall devise a variable-order continuous Galerkin time stepping method which is especially geared towards norm-preserving dynamical systems. In addition, we will provide an a posteriori estimate for the $L^\infty$-error.

Numerical Analysis · Mathematics 2016-05-18 Thomas P. Wihler

In the literature on projection-based nonlinear model order reduction for fluid dynamics problems, it is often claimed that due to modal truncation, a projection-based reduced-order model (PROM) does not resolve the dissipative regime of…

Numerical Analysis · Mathematics 2020-08-10 Sebastian Grimberg , Charbel Farhat , Noah Youkilis

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy

We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model…

Numerical Analysis · Mathematics 2022-04-20 A. Chertock , A. Kurganov , M. Lukáčová-Medviďová , P. Spichtinger , B. Wiebe

The magnetic flow meter is one of the best possible choice for the measurement of flow rate of liquid metals in fast breeder reactors. Due to the associated complexities in the measuring environment, theoretical evaluation of their…

Numerical Analysis · Mathematics 2016-08-04 Sethupathy S , Udaya Kumar

Due to added numerical stabilization (diffusion), the stationary states of numerical methods for hyperbolic problems need not be consistent discretizations of those of the PDEs. A closely related phenomenon is the lack of consistency of…

Numerical Analysis · Mathematics 2025-11-25 Wasilij Barsukow

The present work presents a stable POD-Galerkin based reduced-order model (ROM) for two-dimensional Rayleigh-B\'enard convection in a square geometry for three Rayleigh numbers: $10^4$ (steady state), $3\times 10^5$ (periodic), and $6…

Fluid Dynamics · Physics 2024-02-09 Krishan Chand , Henrik Rosenberger , Benjamin Sanderse

Model order reduction (MOR) is crucial for the design process of integrated circuits. Specifically, the vast amount of passive RLCk elements in electromagnetic models extracted from physical layouts exacerbates the extraction time, the…

The proper orthogonal decomposition (POD) -- a popular projection-based model order reduction (MOR) method -- may require significant model dimensionalities to successfully capture a nonlinear solution manifold resulting from a…

Computational Engineering, Finance, and Science · Computer Science 2024-08-23 Lisa Scheunemann , Erik Faust

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of…

We investigate a two-state conformational conversion system and introduce a novel structure-preserving numerical scheme that couples a local discontinuous Galerkin space discretization with the backward Euler time-integration method. The…

Numerical Analysis · Mathematics 2026-05-20 Paola F. Antonietti , Mattia Corti , Sergio Gómez , Ilaria Perugia

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Machine Learning · Computer Science 2026-01-16 Andrew F. Ilersich , Kevin Course , Prasanth B. Nair

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…

Numerical Analysis · Mathematics 2024-07-17 Julian Koellermeier , Philipp Krah , Jonas Kusch

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

In this work we propose reduced order methods as a reliable strategy to efficiently solve parametrized optimal control problems governed by shallow waters equations in a solution tracking setting. The physical parametrized model we deal…

Numerical Analysis · Mathematics 2023-08-08 Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza