Publications associées à Séparation des variables

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

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 ...

Walter De Gruyter Gmbh2024

Anomalous dissipation and other non-smooth phenomena in fluids

Massimo Sorella

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

Adaptive isogeometric methods with C-1 (truncated) hierarchical splines on planar multi-patch domains

Rafael Vazquez Hernandez

Isogeometric analysis is a powerful paradigm which exploits the high smoothness of splines for the numerical solution of high order partial differential equations. However, the tensor-product structure of standard multivariate B-spline models is not well s ...

WORLD SCIENTIFIC PUBL CO PTE LTD2023

Fast global spectral methods for three-dimensional partial differential equations

Daniel Kressner, Christoph Max Strössner

Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...

OXFORD UNIV PRESS2022

A Continuized View on Nesterov Acceleration

Nicolas Henri Bernard Flammarion, Raphaël Jean Berthier

We introduce the "continuized" Nesterov acceleration, a close variant of Nesterov acceleration whose variables are indexed by a continuous time parameter. The two variables continuously mix following a linear ordinary differential equation and take gradien ...

2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...

EPFL2021

Seamless integration of design and Kirchhoff-Love shell analysis using analysis-suitable unstructured T-splines

Xiaodong Wei, Deepesh Toshniwal

Analysis-suitable T-splines (ASTS) including both extraordinary points and T-junctions are used to solve Kirchhoff-Love shell problems. Extraordinary points are required to represent surfaces with arbitrary topological genus. T-junctions enable local refin ...

ELSEVIER SCIENCE SA2020

Mapping the site-specific accuracy of loop-based local pulse wave velocity estimation and reflection magnitude: a 1D arterial network model analysis

Nikolaos Stergiopoulos, Patrick Segers

Objective: Local pulse wave velocity (PWV) can be estimated from the waterhammer equation and is an essential component of wave separation analysis. However, previous studies have demonstrated inaccuracies in the estimations of local PWV due to the presenc ...

2019

Time and space adaptivity of the wave equation discretized in time by a second-order scheme

Marco Picasso, Olga Gorynina

The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the ...

2019

Learning Feature Maps of the Koopman Operator: A Subspace Viewpoint

Colin Neil Jones, Yingzhao Lian

The Koopman operator was recently shown to be a useful method for nonlinear system identification and controller design. However, the scalability of current data-driven approaches is limited by the selection of feature maps. In this paper, we present a new ...

IEEE2019

A mixture of thermoelastic solids with two temperatures

Maria Masid Barcon

In this work we study, from the numerical point of view, a problem involving one-dimensional thermoelastic mixtures with two different temperatures; that is, when each component of the mixture has its own temperature. The mechanical problem consists of two ...

Pergamon-Elsevier Science Ltd2017

Isogeometric Analysis for High Order Geometric Partial Differential Equations with Applications

Andrea Bartezzaghi

In this thesis, we consider the numerical approximation of high order geometric Partial Differential Equations (PDEs). We first consider high order PDEs defined on surfaces in the 3D space that are represented by single-patch tensor product NURBS. Then, we ...

EPFL2017

Idealized digital models for conical reed instruments, with focus on the internal pressure waveform

Two models for the generation of self-oscillations of reed conical woodwinds are presented. The models use the fewest parameters (of either the resonator or the exciter), whose influence can be quickly explored. The formulation extends iterated maps obtain ...

Acoustical Soc Amer Amer Inst Physics2016

Data Reconciliation in Open Reaction Systems using the Concept of Extents

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan

Kinetic models of chemical reaction systems are typically represented in terms of state variables, such as concentrations, temperature and partial pressures [1]. These state variables in turn depend on the underlying reactions, transfer phenomena, and tran ...

2015

Numerical pancake droplets: from capturing to versatile microfluidics

François Gallaire, Mathias Nagel

This article proposes a numerical model for microfluidic two-phase flows in flat channels, also called Hele-Shaw cells. The initially three-dimensional problem is simplified to two-dimensions by depth averaging in the thin direction. The 2D partial differe ...

SOCIETE HYDROTECHNIQUE DE FRANCE2012

Wavelet Steerability and the Higher-Order Riesz Transform

Michaël Unser, Dimitri Nestor Alice Van De Ville

Our main goal in this paper is to set the foundations of a general continuous-domain framework for designing steerable, reversible signal transformations (a.k.a. frames) in multiple dimensions (d ≥ 2). To that end, we introduce a self-reversible, Nth-order ...

Institute of Electrical and Electronics Engineers2010