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We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…

Numerical Analysis · Mathematics 2019-05-15 Marco Tezzele , Nicola Demo , Gianluigi Rozza

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

This paper focuses on reduced-order models (ROMs) built for the efficient treatment of PDEs having solutions that bifurcate as the values of multiple input parameters change. First, we consider a method called local ROM that uses k-means…

Numerical Analysis · Mathematics 2022-01-03 Martin W. Hess , Annalisa Quaini , Gianluigi Rozza

In this paper, we propose a new stabilized projection-based POD-ROM for the numerical simulation of incompressible flows. The new method draws inspiration from successful numerical stabilization techniques used in the context of Finite…

Numerical Analysis · Mathematics 2019-07-23 Samuele Rubino

Uncertainty quantification (UQ) tasks, such as sensitivity analysis and parameter estimation, entail a huge computational complexity when dealing with input-output maps involving the solution of nonlinear differential problems, because of…

Numerical Analysis · Mathematics 2023-02-17 Ludovica Cicci , Stefania Fresca , Mengwu Guo , Andrea Manzoni , Paolo Zunino

We present a non-intrusive model reduction framework for linear poroelasticity problems in heterogeneous porous media using proper orthogonal decomposition (POD) and neural networks, based on the usual offline-online paradigm. As the…

Numerical Analysis · Mathematics 2023-08-08 T. Kadeethum , F. Ballarin , N. Bouklas

Partial differential equations (PDE) often involve parameters, such as viscosity or density. An analysis of the PDE may involve considering a large range of parameter values, as occurs in uncertainty quantification, control and…

Numerical Analysis · Mathematics 2017-09-28 Max Gunzburger , Nan Jiang , Michael Schneier

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

We apply reduced-order modeling (ROM) techniques to single-phase flow in faulted porous media, accounting for changing rock properties and fault geometry variations using a radial basis function mesh deformation method. This approach…

Numerical Analysis · Mathematics 2024-03-07 Enrico Ballini , Luca Formaggia , Alessio Fumagalli , Anna Scotti , Paolo Zunino

Non-intrusive model reduction is a promising solution to system dynamics prediction, especially in cases where data are collected from experimental campaigns or proprietary software simulations. In this work, we present a method for…

Fluid Dynamics · Physics 2024-04-04 Leonidas Gkimisis , Thomas Richter , Peter Benner

We investigate reduced-order models for acoustic and electromagnetic wave problems in parametrically defined domains. The parameter-to-solution maps are approximated following the so-called Galerkin POD-NN method, which combines the…

Numerical Analysis · Mathematics 2024-06-21 Philipp Weder , Mariella Kast , Fernando Henríquez , Jan S. Hesthaven

In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…

Numerical Analysis · Mathematics 2024-02-21 Ivan Prusak , Davide Torlo , Monica Nonino , Gianluigi Rozza

Projection-based model order reduction of dynamical systems usually introduces an error between the high-fidelity model and its counterpart of lower dimension. This unknown error can be bounded by residual-based methods, which are typically…

Numerical Analysis · Mathematics 2023-03-31 Johannes Rettberg , Dominik Wittwar , Patrick Buchfink , Robin Herkert , Jörg Fehr , Bernard Haasdonk

We apply the Proper Orthogonal Decomposition (POD) method for the efficient simulation of several scenarios undergone by Micro-Electro-Mechanical-Systems, involving nonlinearites of geometric and electrostatic nature. The former type of…

Numerical Analysis · Mathematics 2022-02-22 Gobat G. , Opreni A. , Fresca S. , Manzoni A. , Frangi A

In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…

Computational Physics · Physics 2020-04-22 Suraj Pawar , Shady E. Ahmed , Omer San , Adil Rasheed

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

Reduced order modeling (ROM) aims to mitigate computational complexity by reducing the size of a high-dimensional state space. In this study, we demonstrate the efficiency, accuracy, and stability of proper orthogonal decomposition…

Atmospheric and Oceanic Physics · Physics 2025-04-17 Yusuf Aydogdu , Navaratnam Sri Namachchivaya

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

Quantum nanostructures offer crucial applications in electronics, photonics, materials, drugs, etc. For accurate design and analysis of nanostructures and materials, simulations of the Schrodinger or Schrodinger-like equation are always…

Computational Physics · Physics 2025-07-09 Martin Veresko , Yu Liu , Daqing Hou , Ming-Cheng Cheng

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