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Fabio Nobile

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Publications associées (97)

A quasi-optimal sparse grids procedure for groundwater flows

Fabio Nobile, Lorenzo Tamellini

In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work "On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is model ...

Springer2014

Patient-specific generation of the Purkinje network driven by clinical measurements of a normal propagation

Fabio Nobile, Alfio Quarteroni, Christian Vergara, Elena Faggiano

The propagation of the electrical signal in the Purkinje network is the starting point for the activation of the ventricular muscular cells leading to the contraction of the ventricle. In the computational models, describing the electrical activity of the ...

Springer Verlag2014

Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics

Fabio Nobile, Christian Vergara

In this paper we consider the numerical solution of the three-dimensional fluid–structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, ...

Elsevier2014

Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

2014

Mixed Finite Elements for spatial regression with PDE penalization

Fabio Nobile

We study a class of models at the interface between statistics and numerical analysis. Specifically, we consider nonparametric regression models for the estimation of spatial fields from pointwise and noisy observations, which account for problem-specific ...

2014

Moment equations for the mixed formulation of the Hodge Laplacian with stochastic loading term

Fabio Nobile, Francesca Bonizzoni, Annalisa Buffa

We study the mixed formulation of the stochastic Hodge-Laplace problem dened on a

n

-dimensional domain

D (n ≥ 1)

, with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. We ...

2014

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

Analysis of Discrete L2 Projection on Polynomial Spaces with Random Evaluations

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

We analyse the problem of approximating a multivariate function by discrete least-squares projection on a polynomial space starting from random, noise-free observations. An area of possible application of such technique is Uncertainty Quantification (UQ) f ...

2014

Convergence of quasi-optimal Stochastic Galerkin methods for a class of PDES with random coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we consider quasi-optimal versions of the Stochastic Galerkin method for solving linear elliptic PDEs with stochastic coefficients. In particular, we consider the case of a finite number

N

of random inputs and an analytic dependence of the s ...

2014

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Time accurate partitioned algorithms for the solution of fluid-structure interaction problems in haemodynamics

Fabio Nobile, Christian Vergara

In this work we deal with the numerical solution of the fluid-structure interaction problem arising in the haemodynamic environment. In particular, we consider BDF and Newmark time discretization schemes, and we study different methods for the treatment of ...

2013

A stochastic collocation method for the second order wave equation with a discontinuous random speed

Fabio Nobile

In this paper we propose and analyze a stochastic collocation method for solving the second order wave equation with a random wave speed and subjected to deterministic boundary and initial conditions. The speed is piecewise smooth in the physical space and ...

Springer2013

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

Sparse spectral approximations for computing polynomial functionals

Fabio Nobile

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions th ...

EPFL-SB-MATHICSE2012

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

An active strain electromechanical model for cardiac tissue

Fabio Nobile, Alfio Quarteroni, Ricardo Esteban Ruiz Baier

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the ...

Wiley2012

Electromechanical Coupling In Cardiac Dynamics: The Active Strain Approach

Fabio Nobile, Alfio Quarteroni

The coupling between cardiac mechanics and electric signaling is addressed in a nonstandard framework in which the electrical potential dictates the active strain (not stress) of the muscle. The physiological and mathematical motivations leading us to this ...

Society for Industrial and Applied Mathematics2011

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