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Fabio Nobile

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Related publications (97)

Page 3 of 5

Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We perform a general optimization of the parameters in the multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. We optimize hierarchies with geometric and ...

2016

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

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

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

Fabio Nobile

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximation ...

Springer2018

A technique for non-intrusive greedy piecewise-rational model reduction of frequency response problems over wide frequency bands

Fabio Nobile, Davide Pradovera

In the field of model order reduction for frequency response problems, the minimal rational interpolation (MRI) method has been shown to be quite effective. However, in some cases, numerical instabilities may arise when applying MRI to build a surrogate mo ...

2022

Electromechanical Coupling In Cardiac Dynamics: The Active Strain Approach

Alfio Quarteroni, Fabio Nobile

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

Unbiased Likelihood Estimation of Wright–Fisher Diffusion Processes

Fabio Nobile

In this paper we propose a Monte Carlo maximum likelihood estimation strategy for discretely observed Wright–Fisher diffusions. Our approach provides an unbiased estimator of the likelihood function and is based on exact simulation techniques that are of s ...

Springer Cham2024

A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this article, a finite element error analysis is performed on a class of linear and nonlinear elliptic problems with small uncertain input. Using a perturbation approach, the exact (random) solution is expanded up to a certain order with respect to a pa ...

2016

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

Alfio Quarteroni, Fabio Nobile, 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

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Fabio Nobile, Jürg Alexander Schiffmann, 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 ...

Amer Soc Mechanical Engineers2023

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

Convergence estimates in probability and in expectation for discrete least squares with noisy evaluations at random points

Fabio Nobile, Giovanni Migliorati

We study the accuracy of the discrete least-squares approximation on a finite-dimensional space of a real-valued target function from noisy pointwise evaluations at independent random points distributed according to a given sampling probability measure. Th ...

2015

A new method to interpolate POD reduced bases-Application to the parametric model order reduction of a gas bearings supported rotor

Fabio Nobile, Jürg Alexander Schiffmann, Dimitri Maurice Goutaudier

The proper orthogonal decomposition (POD) is successfully employed in a variety of projection-based methods for parametric model order reduction (pMOR) of large dynamical systems. It extracts the most energetic modes describing the dynamics of a system fro ...

Wiley2023

Regularity and sparse approximation of the recursive first moment equations for the lognormal Darcy problem

Fabio Nobile, Francesca Bonizzoni

We study the Darcy boundary value problem with lognormal permeability field. We adopt a perturbation approach, expanding the solution in Taylor series around the nominal value of the coefficient, and approximating the expected value of the stochastic solut ...

2020

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

Personalized computational electro-mechanics simulations to optimize cardiac resynchronization therapy

Fabio Nobile

In this study, we present a computational framework designed to evaluate virtual scenarios of cardiac resynchronization therapy (CRT) and compare their effectiveness based on relevant clinical biomarkers. Our approach involves electro-mechanical numerical ...

2024

Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Rajesh Kumar, Daniel Kressner, Fabio Nobile, Christine Tobler

Gaussian random fields are widely used as building blocks for modeling stochastic processes. This paper is concerned with the efficient representation of d-point correlations for such fields, which in turn enables the representation of more general stochas ...

2015

Frequency-Domain Non-intrusive Greedy Model Order Reduction Based on Minimal Rational Approximation

Fabio Nobile, Davide Pradovera

We present a technique for Model Order Reduction (MOR) of frequency-domain problems relying on rational interpolation of vector-valued functions. The selection of the sample points is carried out adaptively according to a greedy procedure. We describe seve ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

A multigrid method for PDE-constrained optimization with uncertain inputs

Fabio Nobile, Tommaso Vanzan

In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence analysis of collective ...

Springer Science and Business Media LLC2024

Function Integration, Reconstruction And Approximation Using Rank-1 Lattices

Fabio Nobile, Giovanni Migliorati

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev space, via tent ...

2021