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Shape optimization is a challenging task in many engineering fields, since the numerical solutions of parametric system may be computationally expensive. This work presents a novel optimization procedure based on reduced order modeling,…

Numerical Analysis · Mathematics 2018-11-07 Nicola Demo , Marco Tezzele , Gianluca Gustin , Gianpiero Lavini , Gianluigi Rozza

This contribution describes the implementation of a data--driven shape optimization pipeline in a naval architecture application. We adopt reduced order models (ROMs) in order to improve the efficiency of the overall optimization, keeping a…

Numerical Analysis · Mathematics 2024-01-22 Nicola Demo , Giulio Ortali , Gianluca Gustin , Gianluigi Rozza , Gianpiero Lavini

We present the results of the application of a parameter space reduction methodology based on active subspaces (AS) to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are considered to assess…

Numerical Analysis · Mathematics 2018-11-07 Marco Tezzele , Nicola Demo , Mahmoud Gadalla , Andrea Mola , Gianluigi Rozza

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

Nowadays, the shipbuilding industry is facing a radical change towards solutions with a smaller environmental impact. This can be achieved with low emissions engines, optimized shape designs with lower wave resistance and noise generation,…

Numerical Analysis · Mathematics 2023-11-21 Marco Tezzele , Lorenzo Fabris , Matteo Sidari , Mauro Sicchiero , Gianluigi Rozza

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

While proper orthogonal decomposition (POD) is widely used for model reduction, its standard form does not take into account any parametric model structure. Extensions to POD have been proposed to address this, but these either require…

Numerical Analysis · Mathematics 2025-08-13 Sebastiaan P. C. van Schie , Boris Kramer , John T. Hwang

We propose a new model-order reduction framework to poorly reducible problems arising from parametric partial differential equations with geometric variability. In such problems, the solution manifold exhibits a slowly decaying Kolmogorov…

Numerical Analysis · Mathematics 2025-10-30 Abbas Kabalan , Fabien Casenave , Felipe Bordeu , Virginie Ehrlacher , Alexandre Ern

In this work we propose tailored model order reduction for varying boundary optimal control problems governed by parametric partial differential equations. With varying boundary control, we mean that a specific parameter changes where the…

Numerical Analysis · Mathematics 2024-01-22 Maria Strazzullo , Fabio Vicini

The work provides an integrated pipeline for the model order reduction of turbulent flows around parametrised geometries in aerodynamics. In particular, Free-Form Deformation is applied for geometry parametrisation, whereas two different…

Numerical Analysis · Mathematics 2018-03-15 F. Salmoiraghi , A. Scardigli , H. Telib , G. Rozza

Methodologies for reducing the design-space dimensionality in shape optimization have been recently developed based on unsupervised machine learning methods. These methods provide reduced dimensionality representations of the design space,…

Optimization and Control · Mathematics 2022-12-21 Andrea Serani , Matteo Diez

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

In this paper, we propose a shape optimization pipeline for propeller blades, applied to naval applications. The geometrical features of a blade are exploited to parametrize it, allowing to obtain deformed blades by perturbating their…

Optimization and Control · Mathematics 2024-01-17 Anna Ivagnes , Nicola Demo , Gianluigi Rozza

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Numerical Analysis · Mathematics 2024-05-15 Nicola Rares Franco , Andrea Manzoni , Paolo Zunino , Jan S. Hesthaven

In this contribution, we present the results of the application of a parameter space reduction methodology based on active subspaces to the hull hydrodynamic design problem. Several parametric deformations of an initial hull shape are…

Numerical Analysis · Mathematics 2018-04-04 Nicola Demo , Marco Tezzele , Andrea Mola , Gianluigi Rozza

We present the results of the first application in the naval architecture field of a methodology based on active subspaces properties for parameters space reduction. The physical problem considered is the one of the simulation of the…

Numerical Analysis · Mathematics 2018-10-12 Marco Tezzele , Filippo Salmoiraghi , Andrea Mola , Gianluigi Rozza

We apply an unfitted HDG discretization to a model problem in shape optimization. The method proposed uses a fixed, shape regular, non-geometry conforming mesh and a high order transfer technique to deal with the curved boundaries arising…

Numerical Analysis · Mathematics 2025-09-30 Esteban Henríquez , Tonatiuh Sánchez-Vizuet , Manuel Solano

This paper describes a class of shape optimization problems for optical metamaterials comprised of periodic microscale inclusions composed of a dielectric, low-dimensional material suspended in a non-magnetic bulk dielectric. The shape…

Numerical Analysis · Mathematics 2024-01-08 Manaswinee Bezbaruah , Matthias Maier , Winnifried Wollner

A model-order reduction framework for the meshless smoothed-particle hydrodynamics (SPH) method is presented. The proposed framework introduces the concept of modal reference spaces to overcome the challenges of discovering low-dimensional…

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
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