Reduced basis approximation and error bounds for potential flows in parametrized geometries

Chattez avec Graph Search

Posez n’importe quelle question sur les cours, conférences, exercices, recherches, actualités, etc. de l’EPFL ou essayez les exemples de questions ci-dessous.

AVERTISSEMENT : Le chatbot Graph n'est pas programmé pour fournir des réponses explicites ou catégoriques à vos questions. Il transforme plutôt vos questions en demandes API qui sont distribuées aux différents services informatiques officiellement administrés par l'EPFL. Son but est uniquement de collecter et de recommander des références pertinentes à des contenus que vous pouvez explorer pour vous aider à répondre à vos questions.

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

We develop new tools to study landscapes in nonconvex optimization. Given one optimization problem, we pair it with another by smoothly parametrizing the domain. This is either for practical purposes (e.g., to use smooth optimization algorithms with good g ...

The goal of this work is to use anisotropic adaptive finite elements for the numerical simulation of aluminium electrolysis. The anisotropic adaptive criteria are based on a posteriori error estimates derived for simplified problems. First, we consider an ...

Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...

We present a finite elements-neural network approach for the numerical approximation of parametric partial differential equations. The algorithm generates training data from finite element simulations, and uses a data -driven (supervised) feedforward neura ...

For a high-dimensional problem, a randomized Gram-Schmidt (RGS) algorithm is beneficial in terms of both computational cost and numerical stability. We apply this dimension reduction technique by random sketching to Krylov subspace methods, e.g., to the ge ...

The p-Laplacian problem -del & sdot; ((mu + |del u|(p-2))del u) = f is considered, where mu is a given positive number. An anisotropic a posteriori residual-based error estimator is presented. The error estimator is shown to be equivalent, up to higher ord ...

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Peclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Str ...

An a posteriori error estimator based on an equilibrated flux reconstruction is proposed for defeaturing problems in the context of finite element discretizations. Defeaturing consists in the simplification of a geometry by removing features that are consi ...

A unified numerical framework is presented for the modelling of multiphasic viscoelastic and elastic flows. The rheologies considered range from incompressible Newtonian or Oldroyd-B viscoelastic fluids to Neo-Hookean elastic solids. The model is formulate ...

In this thesis, we propose and analyze novel numerical algorithms for solving three different high-dimensional problems involving tensors. The commonality of these problems is that the tensors can potentially be well approximated in low-rank formats. Ident ...

The effects of apparatus-induced dispersion on nonuniform, density-dependent flow in a cylindrical soil column were investigated using a finite-element model. To validate the model, the results with an analytical solution and laboratory column test data we ...

The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of empirical means of de ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

For the first time, a real-time capable NBI code, which has a comparable fidelity to the much more computationally expensive Monte Carlo codes such as NUBEAM, has been coupled to the discharge control system of a tokamak. This implementation has been done ...

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

Background: Simulating the cardiac function requires the numerical solution of multi-physics and multi-scale mathematical models. This underscores the need for streamlined, accurate, and high-performance computational tools. Despite the dedicated endeavors ...

The objective of this study is to address the difficulty of simplifying the geometric model in which a differential problem is formulated, also called defeaturing, while simultaneously ensuring that the accuracy of the solution is maintained under control. ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

Reduced basis approximation and error bounds for potential flows in parametrized geometries

Chattez avec Graph Search

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

The effect of smooth parametrizations on nonconvex optimization landscapes

Adaptive Finite Elements with Large Aspect Ratio. Application to Aluminium Electrolysis

Learning the intrinsic dynamics of spatio-temporal processes through Latent Dynamics Networks

Error assessment of an adaptive finite elements-neural networks method for an elliptic parametric PDE

Randomized flexible GMRES with deflated restarting

Anisotropic Adaptive Finite Elements for a p-Laplacian Problem

Stability: a search for structure

A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control

An equilibrated flux a posteriori error estimator for defeaturing problems

Numerical simulation of immiscible incompressible viscous, viscoelastic and elastic multiphase flows

Low-Rank Tensor Methods for High-Dimensional Problems

Numerical analysis of apparatus-induced dispersion for density-dependent solute transport in porous media

Tensor approximation of the self-diffusion matrix of tagged particle processes

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

Real-time implementation of the high-fidelity NBI code RABBIT into the discharge control system of ASDEX Upgrade

Analysis-aware defeaturing of complex geometries with Neumann features

lifex-ep: a robust and efficient software for cardiac electrophysiology simulations

A Shape Derivative Approach to Domain Simplification

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems