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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

This paper presents an H2-optimal model order reduction (MOR) method for linear systems with quadratic outputs based on Riemannian optimization. The H2-optimal MOR is formulated as an optimization problem in which the optimization variables…

Optimization and Control · Mathematics 2026-05-12 Xiaolong Wang , Chenglong Liu

We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…

Numerical Analysis · Mathematics 2021-09-28 J. S. Hesthaven , C. Pagliantini , N. Ripamonti

Model reduction using the proper orthogonal decomposition (POD) method is applied to the dynamics of ferroelastic patches to study the first order square to rectangular phase transformations. Governing equations for the system dynamics are…

Materials Science · Physics 2007-05-23 Linxiang X. Wang , Roderick V. N. Melnik

A reduced-order model based on Proper Orthogonal Decomposition (POD) is proposed for the bidomain equations of cardiac electrophysiology. Its accuracy is assessed through electrocardiograms in various configurations, including myocardium…

Numerical Analysis · Mathematics 2012-07-23 Muriel Boulakia , Elisa Schenone , Jean-Frédéric Gerbeau

Spectral proper orthogonal decomposition (SPOD) is an increasingly popular modal analysis method in the field of fluid dynamics due to its specific properties: a linear system forced with white noise should have SPOD modes identical to…

Fluid Dynamics · Physics 2024-02-20 Diego C. P. Blanco , Eduardo Martini , Kenzo Sasaki , André V. G. Cavalieri

This work proposes a novel structure-preserving model order reduction (MOR) method for linear, time-invariant port-Hamiltonian (pH) systems. Our goal is to construct a reduced order pH system, which can still be interpreted in the physical…

Optimization and Control · Mathematics 2025-10-16 Silke Glas , Mir Mamunuzzaman , Hongliang Mu , Hans Zwart

We propose a Proper Orthogonal Decomposition (POD)-Galerkin based Reduced Order Model (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient…

Numerical Analysis · Mathematics 2021-04-14 Michele Girfoglio , Annalisa Quaini , Gianluigi Rozza

In recent years, there has been a growing interest in understanding complex microstructures and their effect on macroscopic properties. In general, it is difficult to derive an effective constitutive law for such microstructures with…

Computational Engineering, Finance, and Science · Computer Science 2023-10-18 Theron Guo , Ondřej Rokoš , Karen Veroy

Model order reduction (MOR) techniques have always struggled in compressing information for advection dominated problems. Their linear nature does not allow to accelerate the slow decay of the Kolmogorov $N$--width of these problems. In the…

Numerical Analysis · Mathematics 2020-04-01 Davide Torlo

Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing equations. While the Lagrangian framework for ROM…

Numerical Analysis · Mathematics 2020-03-30 Hannah Lu , Daniel M. Tartakovsky

We propose a novel stochastic reduced-order model (SROM) for complex systems by combining clustering and classification strategies. Specifically, the distance and centroid of centroidal Voronoi tessellation (CVT) are redefined according to…

Numerical Analysis · Mathematics 2022-04-26 Meixin Xiong , Liuhong Chen , Ju Ming , Zhiwen Zhang

Classical model order reduction (MOR) for parametric problems may become computationally inefficient due to large sizes of the required projection bases, especially for problems with slowly decaying Kolmogorov n-widths. Additionally,…

Numerical Analysis · Mathematics 2024-05-21 Robin Herkert , Patrick Buchfink , Bernard Haasdonk

The numerical simulation of electromagnetic transients in fusion devices is essential for analyzing plasma stability and disruptive events. However, it remains computationally demanding due to the large-scale dense systems arising from…

Numerical Analysis · Mathematics 2026-05-28 Salvatore Ventre

This study presents a framework for estimating the full vibrational state of wind turbine blades from sparse deflection measurements. The identification is performed in a reduced-order space obtained from a Proper Orthogonal Decomposition…

Systems and Control · Electrical Eng. & Systems 2025-04-14 Lorenzo Schena , Wim Munters , Jan Helsen , Miguel A. Mendez

In this paper we consider the numerical approximation of infinite horizon problems via the dynamic programming approach. The value function of the problem solves a Hamilton-Jacobi-Bellman (HJB) equation that is approximated by a fully…

Numerical Analysis · Mathematics 2024-11-06 Javier de Frutos , Bosco Garcia-Archilla , Julia Novo

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

Numerical Analysis · Mathematics 2022-11-01 Bosco García-Archilla , Volker John , Julia Novo

This study presents band-ensemble Spectral Proper Orthogonal Decomposition (bSPOD). The approach is inspired by frequency smoothing, a method used to reduce estimator variance in power spectral density estimates, and is here extended to…

We propose reduced order methods as a suitable approach to face parametrized optimal control problems governed by partial differential equations, with applications in en- vironmental marine sciences and engineering. Environmental…

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

Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…

Computational Physics · Physics 2021-10-25 Saviz Mowlavi , Themistoklis P. Sapsis