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The simulation of complex systems, such as gas transport in large pipeline networks, often involves solving PDEs posed on intricate graph structures. Such problems require considerable computational and memory resources. The Random Batch…

Numerical Analysis · Mathematics 2025-09-01 Martín Hernández

Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…

Numerical Analysis · Mathematics 2022-01-26 Mario Ohlberger , Stephan Rave

In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium…

Numerical Analysis · Mathematics 2021-10-13 M. Landstorfer , M. Ohlberger , S. Rave , M. Tacke

We are interested in numerically approximating the solution ${\bf U}(t)$ of the large dimensional semilinear matrix differential equation $\dot{\bf U}(t) = { \bf A}{\bf U}(t) + {\bf U}(t){ \bf B} + {\cal F}({\bf U},t)$, with appropriate…

Numerical Analysis · Mathematics 2021-05-26 Gerhard Kirsten , Valeria Simoncini

In this paper, we propose a network model, the multiclass classification-based reduced order model (MC-ROM), for solving time-dependent parametric partial differential equations (PPDEs). This work is inspired by the observation of applying…

Numerical Analysis · Mathematics 2022-10-11 Chen Cui , Kai Jiang , Shi Shu

Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…

Numerical Analysis · Mathematics 2024-01-02 Lorenzo Pareschi , Mattia Zanella

We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…

Numerical Analysis · Mathematics 2015-06-23 Remi Abgrall , David Amsallem

Reduced-order modeling (ROM) commonly refers to the construction, based on a few solutions (referred to as snapshots) of an expensive discretized partial differential equation (PDE), and the subsequent application of low-dimensional…

Numerical Analysis · Mathematics 2019-05-22 Martin Hess , Alessandro Alla , Annalisa Quaini , Gianluigi Rozza , Max Gunzburger

The long runtime of high-fidelity partial differential equation (PDE) solvers makes them unsuitable for time-critical applications. We propose to accelerate PDE solvers using reduced-order modeling (ROM). Whereas prior ROM approaches reduce…

We focus on the numerical modelling of water waves by means of depth averaged models. We consider in particular PDE systems which consist in a nonlinear hyperbolic model plus a linear dispersive perturbation involving an elliptic operator.…

Numerical Analysis · Mathematics 2022-11-24 Davide Torlo , Mario Ricchiuto

In gradient-based time domain topology optimization, design sensitivity analysis (DSA) of the dynamic response is essential, and requires high computational cost to directly differentiate, especially for high-order dynamic system. To…

Numerical Analysis · Mathematics 2023-08-22 Shuhao Li , Hu Wang , Jichao Yin , Xinchao Jiang , Yaya Zhang

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…

Numerical Analysis · Mathematics 2022-02-08 Ludovica Cicci , Stefania Fresca , Andrea Manzoni

Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried…

Numerical Analysis · Mathematics 2020-04-02 Wanli He , Philip Avery , Charbel Farhat

In the study of micro-swimmers, both artificial and biological ones, many-query problems arise naturally. Even with the use of advanced high performance computing (HPC), it is not possible to solve this kind of problems in an acceptable…

Numerical Analysis · Mathematics 2020-08-04 Nicola Giuliani , Martin W. Hess , Antonio DeSimone , Gianluigi Rozza

This work investigates a two-stage method for constructing projection-based reduced-order models (ROMs) of parameterized partial differential equations (PDEs). Based on established tensorial ROM methodology, the proposed approach reduces…

Numerical Analysis · Mathematics 2026-04-30 Arjun Vijaywargia , Eric C. Cyr , Anthony Gruber

Reduced-basis methods (RB methods or RBMs) form one of the most promising techniques to deliver numerical solutions of parametrized PDEs in real-time performance with reasonable accuracy. For incompressible flow problems, RBMs based on LBB…

Numerical Analysis · Mathematics 2019-01-30 Eivind Fonn , Harald van Brummelen , Trond Kvamsdal , Adil Rasheed

In this paper, a reduced-order model (ROM) based on the proper orthogonal decomposition and the discrete empirical interpolation method is proposed for efficiently simulating time-fractional partial differential equations (TFPDEs). Both…

Numerical Analysis · Mathematics 2024-02-07 Hongfei Fu , Hong Wang , Zhu Wang

A bottleneck for computational lithography and optical metrology are long computational times for near field simulations. For design, optimization, and inverse scatterometry usually the same basic layout has to be simulated multiple times…

Optics · Physics 2010-11-12 J. Pomplun , L. Zschiedrich , S. Burger , F. Schmidt

We are concerned with employing Model Order Reduction (MOR) to efficiently solve parameterized multiscale problems using the Localized Orthogonal Decomposition (LOD) multiscale method. Like many multiscale methods, the LOD follows the idea…

Numerical Analysis · Mathematics 2023-07-13 Tim Keil , Stephan Rave

Hyper-reduction methods have gained increasing attention for their potential to accelerate reduced order models for nonlinear systems, yet their comparative accuracy and computational efficiency are not well understood. Motivated by this…

Mathematical Software · Computer Science 2026-03-02 Axel Larsson , Minji Kim , Chris Vales , Sigrid Adriaenssens , Dylan Matthew Copeland , Youngsoo Choi , Siu Wun Cheung