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Fabio Nobile

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Related publications (97)

Page 5 of 5

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Jürg Alexander Schiffmann, Fabio Nobile, Dimitri Maurice Goutaudier

Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requi ...

2023

Continuation Multilevel Monte Carlo Evolutionary Algorithm for Robust Aerodynamic Shape Design

Fabio Nobile, Pénélope Leyland, Michele Pisaroni

The majority of problems in aircraft production and operation require decisions made in the presence of uncertainty. For this reason, aerodynamic designs obtained with traditional deterministic optimization techniques seeking only optimality in a specific ...

2019

Quantifying uncertain system outputs via the multilevel Monte Carlo method — Part I: Central moment estimation

Fabio Nobile, Sebastian Krumscheid, Michele Pisaroni

In this work we introduce and analyze a novel multilevel Monte Carlo (MLMC) estimator for the accurate approximation of central moments of system outputs affected by uncertainties. Central moments play a central role in many disciplines to characterize a r ...

2020

Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures

Fabio Nobile, Sebastian Krumscheid, Sundar Subramaniam Ganesh, Quentin Olivier Martin Ayoul--Guilmard

In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called conditional-value-at-risk, of output quantities of complex random differential models by the MLM ...

2023

Analysis of a Class of Multilevel Markov Chain Monte Carlo Algorithms Based on Independent Metropolis–Hastings

Fabio Nobile, Juan Pablo Madrigal Cianci

In this work, we present, analyze, and implement a class of multilevel Markov chain Monte Carlo(ML-MCMC) algorithms based on independent Metropolis--Hastings proposals for Bayesian inverse problems. In this context, the likelihood function involves solving ...

2023

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

American Mathematical Society (AMS)2025

Partitioned Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

Fabio Nobile, Christian Vergara

We consider the fluid-structure interaction problem arising in haemodynamic applications. The finite elasticity equations for the vessel are written in Lagrangian form, while the Navier-Stokes equations for the blood in Arbitrary Lagrangian Eulerian form. ...

Birkhäuser-Verlag, Springer2012

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 (PDE) with a random coefficient solved with the stochastic collocation finite element method (SC-FEM). The random diffusion coefficient is assumed to depend in an affine way on independent ...

2018

On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

Fabio Nobile

In the framework of stochastic processes, the connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and a recently proposed control approach based on the Fokker-Planck equation is discussed. Under appropriate assum ...

2014

Comparison of Clenshaw-Curtis and Leja Quasi-Optimal Sparse Grids for the Approximation of Random PDEs

Fabio Nobile, Lorenzo Tamellini

In this work we compare different families of nested quadrature points, i.e. the classic Clenshaw-Curtis and various kinds of Leja points, in the context of the quasi-optimal sparse grid approximation of random elliptic PDEs. Numerical evidence suggests th ...

Springer2015

Petrov-Galerkin Dynamical Low Rank Approximation: SUPG stabilisation of advection-dominated problems

Fabio Nobile, Thomas Simon Spencer Trigo Trindade

We propose a novel framework of generalised Petrov-Galerkin Dynamical Low Rank Approximations (DLR) in the context of random PDEs. It builds on the standard Dynamical Low Rank Approximations in their Dynamically Orthogonal formulation. It allows to seamles ...

Elsevier BV2025

Numerical Methods For Uncertainty Quantification

Fabio Nobile

Begell House Inc2015

Analytic regularity and collocation approximation for elliptic PDEs with Random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

2016

Quantifying uncertainties in contact mechanics of rough surfaces using the multilevel Monte Carlo method

Fabio Nobile, Sebastian Krumscheid, Valentine Ginette Madeleine Rey

We quantify the effect of uncertainties on quantities of interest related to contact mechanics of rough surfaces. Specifically, we consider the problem of frictionless non adhesive normal contact between two semi infinite linear elastic solids subject to u ...

2019

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

Fabio Nobile, Lorenzo Tamellini

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...

World Scientific Publ Co Pte Ltd2012

A Multi Level Monte Carlo Algorithm for the Treatment of Geometrical and Operational Uncertainties in Internal and External Aerodynamics

Fabio Nobile, Pénélope Leyland, Michele Pisaroni

In this work we present an efficient Multi Level Monte Carlo (MLMC) algorithm capable of propagating operational uncertainties, due to atmospheric variability of external aerodynamics flows and geometrical uncertainties due to manufacturing tolerances and ...

AIAA2016