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We present a low-order modeling technique for actuated flows based on the regularization of an inverse problem. The inverse problem aims at minimizing the error between the model predictions and some reference simulations. The parameters to…

Fluid Dynamics · Physics 2009-11-13 Jessie Weller , Edoardo Lombardi , Angelo Iollo

This work describes the implementation of a data-driven approach for the reduction of the complexity of parametrical partial differential equations (PDEs) employing Proper Orthogonal Decomposition (POD) and Gaussian Process Regression…

Numerical Analysis · Mathematics 2024-01-22 Giulio Ortali , Nicola Demo , Gianluigi Rozza

In several studies it has been observed that, when using stabilised $\mathbb{P}_k^{}\times\mathbb{P}_k^{}$ elements for both velocity and pressure, the error for the pressure is smaller, or even of a higher order in some cases, than the one…

Numerical Analysis · Mathematics 2020-09-23 Gabriel R. Barrenechea , Michał Bosy , Victorita Dolean

In this paper we consider a reduced order method for the approximation of the eigensolutions of the Laplace problem with Dirichlet boundary condition. We use a time continuation technique that consists in the introduction of a fictitious…

Numerical Analysis · Mathematics 2022-12-14 Fleurianne Bertrand , Daniele Boffi , Abdul Halim

This article contributes to a framework for a computational indirect method based on the Pontryagin maximum principle to efficiently solve a class of state constrained time-optimal control problems in the presence of a time-dependent flow…

Optimization and Control · Mathematics 2022-06-30 Roman Chertovskih , Nathalie T. Khalil , Fernando Lobo Pereira

The fully discrete adjoint equations and the corresponding adjoint method are derived for a globally high- order accurate discretization of conservation laws on parametrized, deforming domains. The conservation law on the deforming domain…

Optimization and Control · Mathematics 2016-09-20 Matthew J. Zahr , Per-Olof Persson

In this paper, we consider a state constrained optimal control problem governed by the transient Stokes equations. The state constraint is given by an L2 functional in space, which is required to fulfill a pointwise bound in time. The…

Numerical Analysis · Mathematics 2026-05-20 Dmitriy Leykekhman , Boris Vexler , Jakob Wagner

Geophysical flow simulations using hyperbolic shallow water moment equations require an efficient discretization of a potentially large system of PDEs, the so-called moment system. This calls for tailored model order reduction techniques…

Numerical Analysis · Mathematics 2024-07-17 Julian Koellermeier , Philipp Krah , Jonas Kusch

A methodology grounded in model reduction is presented for accelerating the gradient-based solution of a family of linear or nonlinear constrained optimization problems where the constraints include at least one linear Partial Differential…

Numerical Analysis · Mathematics 2020-04-15 Youngsoo Choi , Gabriele Boncoraglio , Spenser Anderson , David Amsallem , Charbel Farhat

Geometrically parametrized Partial Differential Equations are nowadays widely used in many different fields as, for example, shape optimization processes or patient specific surgery studies. The focus of this work is on some advances for…

Fluid Dynamics · Physics 2021-07-21 Matteo Zancanaro , Markus Mrosek , Giovanni Stabile , Carsten Othmer , Gianluigi Rozza

A wide range of implicit time integration methods, including multi-step, implicit Runge-Kutta, and Galerkin finite-time element schemes, is evaluated in the context of chaotic dynamical systems. The schemes are applied to solve the Lorenz…

Computational Physics · Physics 2024-01-02 Viktoriya Morozova , James G. Coder , Kevin Holst

We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…

Numerical Analysis · Mathematics 2020-05-19 Oleg Balabanov , Anthony Nouy

This paper considers the optimal boundary control of chemical systems described by advection-diffusion-reaction (ADR) equations. We use a discontinuous Galerkin finite element method (DG-FEM) for the spatial discretization of the governing…

Numerical Analysis · Mathematics 2024-11-27 Marcus Johan Schytt , John Bagterp Jørgensen

Variational approaches have been used successfully as a strategy to take advantage from real data measurements. In several applications, this approach gives a means to increase the accuracy of numerical simulations. In the particular case…

Optimization and Control · Mathematics 2015-10-15 Telma Guerra , Adélia Sequeira , Jorge Tiago

This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The…

Fluid Dynamics · Physics 2023-06-21 Xiaoming Zheng , Weiwei Hu , Jiahong Wu

This paper deals with the numerical modeling of flow around and through a porous obstacle by a reduced order model (ROM) obtained by Galerkin projection of the Navier-Stokes equations onto a Proper Orthogonal Decomposition (POD) reduced…

Fluid Dynamics · Physics 2023-07-24 Cyrille Allery , Claudine Beghein , Claire Dubot , Fabien Dubot

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…

Numerical Analysis · Mathematics 2019-11-19 Giovanni Stabile , Bojana Rosic

In this paper, we investigate an optimal control problem governed by parabolic equations with measure-valued controls over time. We establish the well-posedness of the optimal control problem and derive the first-order optimality condition…

Optimization and Control · Mathematics 2024-04-04 Wei Gong , Dongdong Liang

We consider the optimal control problem governed by diffusion convection reaction equation without control constraints. The proper orthogonal decomposition(POD) method is used to reduce the dimension of the problem. The POD method may be…

Optimization and Control · Mathematics 2015-05-21 Tuğba Akman

This article concerns the problem of computing solutions to state-constrained optimal control problems whose trajectory is affected by a flow field. This general mathematical framework is particularly pertinent to the requirements…

Optimization and Control · Mathematics 2022-06-30 Roman Chertovskih , Nathalie T. Khalil , Dmitry Karamzin , Fernando Lobo Pereira