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Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

Fluid Dynamics · Physics 2024-01-12 X. Lin , D. Xiao , F. Fang

Data-driven modal decompositions are useful tools for compressing data or identifying dominant structures. Popular ones like the dynamic mode decomposition (DMD) and the proper orthogonal decomposition (POD) are defined with continuous…

Fluid Dynamics · Physics 2025-11-06 Manuel Ratz , Alessandro Parente , Miguel Alfonso Mendez

Integration of physics principles with data-driven methods has attracted great attention in recent few years. In this study, a physics-informed dynamic mode decomposition (piDMD) method, where the mass conservation law is integrated with a…

Fluid Dynamics · Physics 2023-11-07 Dandan Li , Bidan Zhao , Shuai Lu , Junwu Wang

In our previous work [Singler, SIAM J. Numer. Anal. 52 (2014), no. 2, 852-876], we considered the proper orthogonal decomposition (POD) of time varying PDE solution data taking values in two different Hilbert spaces. We considered various…

Numerical Analysis · Mathematics 2021-02-01 Sarah Locke , John Singler

Most of the studies on pressure fluctuations in wall-bounded turbulent flows aim at obtaining statistics as power spectra and scaling laws, especially at the walls. In the present study we study energetic coherent pressure structures of…

Fluid Dynamics · Physics 2024-07-23 F. R. Amaral , A. V. G. Cavalieri

We introduce fluctuating hydrodynamics approaches on surfaces for capturing the drift-diffusion dynamics of particles and microstructures immersed within curved fluid interfaces of spherical shape. We take into account the interfacial…

Soft Condensed Matter · Physics 2023-10-24 David Rower , Misha Padidar , Paul J. Atzberger

Mode-based model-reduction is used to reduce the degrees of freedom of high dimensional systems, often by describing the system state by a linear combination of spatial modes. Transport dominated phenomena, ubiquitous in technical and…

Numerical Analysis · Mathematics 2020-02-28 Julius Reiss

Understanding flow structures in urban areas is widely recognized as a challenging concern due to its effect on urban development, air quality, and pollutant dispersion. In this study, state-of-the-art data-driven methods for modal analysis…

We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…

Numerical Analysis · Mathematics 2018-12-27 Robert Altmann , Eric Chung , Roland Maier , Daniel Peterseim , Sai-Mang Pun

This chapter describes modal decompositions in the framework of matrix factorizations. We highlight the differences between classic space-time decompositions and 2D discrete transforms and discuss the general architecture underpinning…

Numerical Analysis · Mathematics 2022-08-29 Miguel A. Mendez

This paper provides an a~priori error analysis of a localized orthogonal decomposition method (LOD) for the numerical stochastic homogenization of a model random diffusion problem. If the uniformly elliptic and bounded random coefficient…

Numerical Analysis · Mathematics 2020-12-03 Julian Fischer , Dietmar Gallistl , Daniel Peterseim

This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…

Optimization and Control · Mathematics 2025-07-01 Yuta Tanabe , Kentaro Yaji , Kuniharu Ushijima

We introduce the stochastic band structure, a method giving the dispersion relation for waves propagating in periodic media or along waveguides, and subject to material loss or radiation damping. Instead of considering an explicit or…

Computational Physics · Physics 2023-06-30 Vincent Laude , Maria E. Korotyaeva

In this paper, we present a Localized Orthogonal Decomposition (LOD) in Petrov-Galerkin formulation for a two-scale Helmholtz-type problem. The two-scale problem is, for instance, motivated from the homogenization of the Helmholtz equation…

Numerical Analysis · Mathematics 2017-03-01 Mario Ohlberger , Barbara Verfürth

Temporal networks, defined as sequences of time-aggregated adjacency matrices, sample latent graph dynamics and trace trajectories in graph space. By interpreting each adjacency matrix as a different time snapshot of a scalar field,…

Data Analysis, Statistics and Probability · Physics 2026-02-27 Lucas Lacasa

This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…

Fluid Dynamics · Physics 2023-08-15 Marin Lauber , Gabriel D. Weymouth , Georges Limbert

The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…

Numerical Analysis · Mathematics 2024-12-20 Steffen Kastian , Dieter Moser , Stefanie Reese , Lars Grasedyck

Proper orthogonal decomposition (POD) stabilized methods for the Navier-Stokes equations are considered and analyzed. We consider two cases, the case in which the snapshots are based on a non inf-sup stable method and the case in which the…

Numerical Analysis · Mathematics 2020-06-02 Julia Novo , Samuele Rubino

This work focuses on the development and analysis of a partitioned numerical method for moving domain, fluid-structure interaction problems. We model the fluid using incompressible Navier-Stokes equations, and the structure using linear…

Numerical Analysis · Mathematics 2020-07-03 Anyastassia Seboldt , Martina Bukač

We introduce two global-in-time domain decomposition methods, namely the Steklov-Poincare method and the Robin method, for solving a fluid-structure interaction system. These methods allow us to formulate the coupled system as a space-time…

Numerical Analysis · Mathematics 2024-08-07 Hemanta Kunwar , Hyesuk Lee