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We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

Numerical Analysis · Mathematics 2019-12-25 Christopher Beattie , Serkan Gugercin , Zoran Tomljanovic

We extend a localized model order reduction method for the distributed finite element solution of elliptic boundary value problems in the cloud. We give a computationally efficient technique to compute the required inner product matrices…

Numerical Analysis · Mathematics 2025-04-01 Tom Gustafsson , Antti Hannukainen , Vili Kohonen

In this paper, we propose a certified reduced basis (RB) method for quasilinear elliptic problems together with its application to nonlinear magnetostatics equations, where the later model permanent magnet synchronous motors (PMSM). The…

Numerical Analysis · Mathematics 2020-07-03 Michael Hinze , Denis Korolev

We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code…

Numerical Analysis · Mathematics 2023-01-02 Eki Agouzal , Jean-Philippe Argaud , Michel Bergmann , Guilhem Ferté , Tommaso Taddei

The aim of this article is to propose a new reduced-order modelling approach for parametric eigenvalue problems arising in electronic structure calculations. Namely, we develop nonlinear reduced basis techniques for the approximation of…

Numerical Analysis · Mathematics 2025-11-19 Maxime Dalery , Genevieve Dusson , Virginie Ehrlacher , Alexei Lozinski

We develop and analyze a nonlinear reduced basis (RB) method for parametrized elliptic partial differential equations based on a binary-tree partition of the parameter domain into tensor-product structured subdomains. Each subdomain is…

Numerical Analysis · Mathematics 2025-11-04 Mohamed Barakat , Diane Guignard

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…

Computational Engineering, Finance, and Science · Computer Science 2024-02-20 Moritz von Tresckow , Herbert De Gersem , Dimitrios Loukrezis

In this paper, we develop a nonlinear reduction framework based on our recently introduced extended group finite element method. By interpolating nonlinearities onto approximation spaces defined with the help of finite elements, the…

Numerical Analysis · Mathematics 2021-06-07 Kevin Tolle , Nicole Marheineke

We propose a new model reduction framework for problems that exhibit transport phenomena. As in the moving finite element method (MFEM), our method employs time-dependent transformation operators and, especially, generalizes MFEM to…

Numerical Analysis · Mathematics 2020-10-30 Felix Black , Philipp Schulze , Benjamin Unger

Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine…

Signal Processing · Electrical Eng. & Systems 2020-03-06 Ion Matei , Johan de Kleer , Alexander Feldman , Rahul Rai , Souma Chowdhury

Conventional offline training of reduced-order bases in a predetermined region of a parameter space leads to parametric reduced-order models that are vulnerable to extrapolation. This vulnerability manifests itself whenever a queried…

Numerical Analysis · Mathematics 2020-04-02 Wanli He , Philip Avery , Charbel Farhat

We present an adaptive reduced-order model for the efficient time-resolved simulation of fluid-structure interaction problems with complex and non-linear deformations. The model is based on repeated linearizations of the structural balance…

Fluid Dynamics · Physics 2020-04-13 Ali Thari , Vito Pasquariello , Niels Aage , Stefan Hickel

In many applications, projection-based reduced-order models (ROMs) have demonstrated the ability to provide rapid approximate solutions to high-fidelity full-order models (FOMs). However, there is no a priori assurance that these…

Numerical Analysis · Computer Science 2020-04-22 Philip A. Etter , Kevin T. Carlberg

We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…

Numerical Analysis · Mathematics 2021-05-27 Cecilia Pagliantini

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

Optimization and Control · Mathematics 2025-05-16 Matteo Tomasetto , Andrea Manzoni , Francesco Braghin

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time,…

Numerical Analysis · Mathematics 2023-02-02 Fabien Casenave , Nissrine Akkari , Felipe Bordeu , Christian Rey , David Ryckelynck

In this work we focus on two different methods to deal with parametrized partial differential equations in an efficient and accurate way. Starting from high fidelity approximations built via the hierarchical model reduction discretization,…

Numerical Analysis · Mathematics 2023-08-08 Matteo Zancanaro , Francesco Ballarin , Simona Perotto , Gianluigi Rozza

We consider the computation of averaged coefficients for the homogenization of elliptic partial differential equations. In this problem, like in many multiscale problems, a large number of similar computations parametrized by the…

Numerical Analysis · Mathematics 2016-08-14 Sébastien Boyaval

We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…

Optimization and Control · Mathematics 2019-09-24 Alessandro Alla , Michael Hinze , Philip Kolvenbach , Oliver Lass , Stefan Ulbrich

In many areas of engineering, nonlinear numerical analysis is playing an increasingly important role in supporting the design and monitoring of structures. Whilst increasing computer resources have made such formerly prohibitive analyses…

Numerical Analysis · Mathematics 2020-07-02 Thomas Simpson , Nikolaos Dervilis , Eleni Chatzi