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Dynamic mechanical metamaterials (MMs) are artificial media composed of periodic micro-structures, designed to manipulate wave propagation. Modeling and designing these materials can be computationally demanding due to the broad design…

Applied Physics · Physics 2023-07-04 Weidi Wang , Alireza Amirkhizi

Highly accurate simulations of complex phenomena governed by partial differential equations (PDEs) typically require intrusive methods and entail expensive computational costs, which might become prohibitive when approximating steady-state…

Machine Learning · Computer Science 2023-05-17 Paolo Conti , Giorgio Gobat , Stefania Fresca , Andrea Manzoni , Attilio Frangi

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…

Machine Learning · Computer Science 2023-06-28 G. I. Drakoulas , T. V. Gortsas , G. C. Bourantas , V. N. Burganos , D. Polyzos

In this paper we consider the numerical approximation of a semilinear reaction-diffusion model problem (PDEs) by means of reduced order methods (ROMs) based on proper orthogonal decomposition (POD). We focus on the time integration of the…

Numerical Analysis · Mathematics 2026-03-05 Bosco García-Archilla , Alicia García-Mascaraque , Julia Novo

A previously developed quantum reduced-order model is revised and applied, together with the domain decomposition, to develop the quantum element method (QEM), a methodology for fast and accurate simulation of quantum eigenvalue problems.…

Computational Physics · Physics 2023-04-18 Ming-C. Cheng

In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…

Numerical Analysis · Mathematics 2023-12-06 Fabian Key , Max von Danwitz , Francesco Ballarin , Gianluigi Rozza

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…

Predictive modeling involving simulation and sensor data at the same time, is a growing challenge in computational science. Even with large-scale finite element models, a mismatch to the sensor data often remains, which can be attributed to…

Computational Engineering, Finance, and Science · Computer Science 2025-12-01 Lucas Hermann , Matthias Bollhöfer , Ulrich Römer

In the reduced order modeling (ROM) framework, the solution of a parametric partial differential equation is approximated by combining the high-fidelity solutions of the problem at hand for several properly chosen configurations. Examples…

Numerical Analysis · Mathematics 2019-05-16 Nicola Demo , Marco Tezzele , Andrea Mola , Gianluigi Rozza

We developed a novel reduced-order multi-scale method for solving large time-domain wavefield simulation problems. Our algorithm consists of two main stages. During the first "off-line" stage the fine-grid operator (of the graph Laplacian…

Numerical Analysis · Mathematics 2017-03-28 Vladimir Druskin , Alexander V. Mamonov , Mikhail Zaslavsky

Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…

Numerical Analysis · Mathematics 2023-07-04 Jun Sur Richard Park , Xueyu Zhu

This paper proposes a model order reduction method for a class of parametric dynamical systems. Using a temporal Fourier transform, we reformulate these systems into complex-valued elliptic equations in the frequency domain, containing…

Numerical Analysis · Mathematics 2026-02-10 Yuming Ba , Liang Chen , Yaru Chen , Qiuqi Li

The investigation of fluid-solid systems is very important in a lot of industrial processes. From a computational point of view, the simulation of such systems is very expensive, especially when a huge number of parametric configurations…

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

Numerical Analysis · Mathematics 2019-11-19 Nicola Demo , Marco Tezzele , Gianluigi Rozza

The real-time monitoring of the structural displacement of the Vacuum Vessel (VV) of thermonuclear fusion devices caused by electromagnetic (EM) loads is of great interest. In this paper, Model Order Reduction (MOR) is applied to the…

Numerical Analysis · Mathematics 2024-05-03 Francesco Lucchini , Alessandro Frescura , Riccardo Torchio , Piergiorgio Alotto , Paolo Bettini

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…

Numerical Analysis · Mathematics 2022-11-10 Zhichao Peng , Yanlai Chen , Yingda Cheng , Fengyan Li

This study concerns the development of a data-based compact model for the prediction of the fluid temperature evolution in district heating (DH) pipeline networks. This so-called "reduced-order model" (ROM) is obtained from reduction of the…

Numerical Analysis · Mathematics 2022-11-28 Mengting Jiang , Michel Speetjens , Camilo Rindt , David Smeulders

Finite-difference time-domain (FDTD) is an effective algorithm for resolving Maxwell equations directly in time domain. Although FDTD has obtained sufficient development, there still exists some improvement space for it, such as…

Computational Physics · Physics 2023-03-29 Huicheng Guo , Henglei Du , Chengpu Liu

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be…

Fluid Dynamics · Physics 2021-11-24 Stefania Fresca , Andrea Manzoni