Publications associées à Calcul scientifique et quantification de l'incertitude - Chaire CADMOS

Porto renaît. Piscine de Porto (Portugal)

Porto renaît, elle se reconstruit. Aujourd’hui, après des années d’oubli et d'abandon, la ville s’extrait brutalement de sa torpeur. Ce changement radical, porté par un tourisme grandissant, favorise la spéculation immobilière: les bâtiments abandonnés et ...

2018

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We analyze the accuracy of the discrete least-squares approximation of a function

u

in multivariate polynomial spaces

P_\Lambda:=span\{y\mapsto y^\nu \,: \, \nu\in \Lambda\}

with

\Lambda\subset N_0^d

over the domain

\Gamma:=[-1,1]^d

, based on the s ...

2017

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

We consider finite element error approximations of the steady incompressible Navier-Stokes equations defined on a randomly perturbed domain, the perturbation being small. Introducing a random mapping, these equations are transformed into PDEs on a fixed re ...

Elsevier2017

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

Fabio Nobile, Diane Sylvie Guignard

In this work, we consider an elliptic partial differential equation with a random coefficient solved with the stochastic collocation finite element method. The random diffusion coefficient is assumed to depend in an affine way on independent random variabl ...

MATHICSE2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

Multi Level Monte Carlo Methods for Uncertainty Quantification and Robust Design Optimization in Aerodynamics

Michele Pisaroni

The vast majority of problems that arise in aircraft production and operation require decisions to be made in the presence of uncertainty. An effective and accurate quantification and control of the level of uncertainty introduced in the design phase and d ...

EPFL2017

Multilevel weighted least squares polynomial approximation

Fabio Nobile

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...

2017

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Fabio Nobile

Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required to achieve quasi ...

MATHICSE2017

Calcul scientifique et quantification de l'incertitude - Chaire CADMOS

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Porto renaît. Piscine de Porto (Portugal)

Dynamical Low Rank approximation of PDEs with random parameters

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

A posteriori error estimation for the steady Navier-Stokes equations in random domains

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Multi Level Monte Carlo Methods for Uncertainty Quantification and Robust Design Optimization in Aerodynamics

Multilevel weighted least squares polynomial approximation

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Porto renaît. Piscine de Porto (Portugal)

A posteriori error estimation for the steady Navier-Stokes equations in random domains

Multi Level Monte Carlo Methods for Uncertainty Quantification and Robust Design Optimization in Aerodynamics

Discrete least-squares approximations over optimized downward closed polynomial spaces in arbitrary dimension

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Dynamical Low Rank approximation of PDEs with random parameters

MATHICSE Technical Report : A posteriori error estimation for the stochastic collocation finite element method

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

MATHICSE Technical Report : Multilevel weighted least squares polynomial approximation

Multilevel weighted least squares polynomial approximation