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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

We consider model order reduction based on proper orthogonal decomposition (POD) for unsteady incompressible Navier-Stokes problems, assuming that the snapshots are given by spatially adapted finite element solutions. We propose two…

Numerical Analysis · Mathematics 2019-08-02 Carmen Gräßle , Michael Hinze , Jens Lang , Sebastian Ullmann

Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…

Machine Learning · Computer Science 2025-12-24 Shane X. Coffing , John Tipton , Arvind T. Mohan , Darren Engwirda

We propose a new algorithm to compute a shifted proper orthogonal decomposition (sPOD) for systems dominated by multiple transport velocities. The sPOD is a recently proposed mode decomposition technique which overcomes the poor performance…

Numerical Analysis · Mathematics 2018-03-06 Philipp Schulze , Julius Reiss , Volker Mehrmann

In this work, we propose a Proper Orthogonal Decomposition-Reduced Order Model (POD-ROM) applied to time-splitting schemes for solving the Navier-Stokes equations with open boundary conditions. In this method, we combine three strategies to…

Numerical Analysis · Mathematics 2025-06-13 Mejdi Azaïez , Tomás Chacón Rebollo , Carlos Núñez Fernández , Samuele Rubino

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

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…

The fluid flow around a bluff body is complex and time dependent, which also contains a wide range of time and length scales. The first few eigenmodes of the proper orthogonal decomposition (POD) of such a flow provide significant insight…

Fluid Dynamics · Physics 2021-11-10 Jahrul Alam , Asokan Variyath

We study reduced-order models of three-dimensional perturbations in linearized channel flow using balanced proper orthogonal decomposition (BPOD). The models are obtained from three-dimensional simulations in physical space as opposed to…

Optimization and Control · Mathematics 2009-11-13 Miloš Ilak , Clarence W. Rowley

This paper describes the numerical implementation in a high-performance computing environment of an open-source library for model order reduction in fluid dynamics. This library, called pyLOM, contains the algorithms of proper orthogonal…

We investigate the sensitivity of reduced order models (ROMs) to training data resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive…

Fluid Dynamics · Physics 2020-07-15 Shady E. Ahmed , Omer San , Diana A. Bistrian , Ionel M. Navon

In this work, the space-time MORe DWR (Model Order Reduction with Dual-Weighted Residual error estimates) framework is extended and further developed for single-phase flow problems in porous media. Specifically, our problem statement is the…

Numerical Analysis · Mathematics 2023-11-16 Hendrik Fischer , Julian Roth , Ludovic Chamoin , Amelie Fau , Mary F. Wheeler , Thomas Wick

We consider integrated circuits with semiconductors modeled by modified nodal analysis and drift-diffusion equations. The drift-diffusion equations are discretized in space using mixed finite element method. This discretization yields a…

Numerical Analysis · Mathematics 2010-03-03 Michael Hinze , Martin Kunkel

This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical…

Atmospheric and Oceanic Physics · Physics 2013-10-08 Omer San , Anne E. Staples , Zhu Wang , Traian Iliescu

A phase proper orthogonal decomposition (Phase POD) method is demonstrated, utilizing phase averaging for the decomposition of spatio-temporal behaviour of statistically non-stationary turbulent flows in an optimized manner. The proposed…

Fluid Dynamics · Physics 2024-03-01 Yisheng Zhang , Azur Hodzic , Fabien Evrard , Berend Van Wachem , Clara M. Velte

We consider proper orthogonal decomposition (POD) methods to approximate the incompressible Navier-Stokes equations. We study the case in which one discretization for the nonlinear term is used in the snapshots (that are computed with a…

Numerical Analysis · Mathematics 2022-03-30 Bosco García-Archilla , Julia Novo , Samuele Rubino

This paper studies the numerical approximation of parametric time-dependent partial differential equations (PDEs) by proper orthogonal decomposition reduced order models (POD-ROMs). Although many papers in the literature consider reduced…

Numerical Analysis · Mathematics 2025-04-28 Bosco García-Arcilla , Alicia García-Mascaraque , Julia Novo

This article presents a Galerkin projection-based reduced-order modelling (ROM) approach for segregated fluid-structure interaction (FSI) problems, formulated within an Arbitrary Lagrangian Eulerian (ALE) framework at low Reynolds numbers…

Numerical Analysis · Mathematics 2025-07-24 Valentin Nkana Ngan , Giovanni Stabile , Andrea Mola , Gianluigi Rozza

POD-DL-ROMs have been recently proposed as an extremely versatile strategy to build accurate and reliable reduced order models (ROMs) for nonlinear parametrized partial differential equations, combining (i) a preliminary dimensionality…

Numerical Analysis · Mathematics 2023-05-09 Simone Brivio , Stefania Fresca , Nicola Rares Franco , Andrea Manzoni

In this study, we explore the effect of basis functions on the performance and convergence of the Galerkin projection-based reduced-order model (ROM) in the minimal flow unit of Couette flow. POD (proper orthogonal decomposition) modes…

Fluid Dynamics · Physics 2026-03-04 Zilin Zong , Igor Maia , André Cavalieri , Yongyun Hwang