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In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g., the Helmholtz equation. In this res ...

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 ...

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 ...

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 ...

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 ...

In this technical report we apply the Continuation Multi Level Monte Carlo (C-MLMC) algorithm to efficiently propagate operating and geometric uncertainties in internal and external aerodynamic simulations modeled by RANS. In particular, we discuss the construction of suitable mesh hierarchies and test the C-MLMC algorithm on the 2D RAE-2822 transonic airfoil and the 3D NASA Rotor 37 affected by operating uncertainties

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 ...

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 ...

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. ...

In this work we explore the extension of the quasi-optimal sparse grids method proposed in our previous work \On the optimal polynomial ap- proximation of stochastic PDEs by Galerkin and Collocation methods" to a Darcy problem where the permeability is modeled as a lognormal random field. We propose an explicit a-priori/a-posteriori procedure for the construc- tion of such quasi-optimal grid and show its effectivenenss on a numerical ex- ample. In this approach, the two main ingredients are an estimate of t

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 ...

In this work we compare numerically 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 that the performances of both families are essentially comparable within such framework.

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...

Fabio Nobile

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Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Continuation Multilevel Monte Carlo Evolutionary Algorithm for Robust Aerodynamic Shape Design

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

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

MATHICSE Technical Report : Continuation Multi-Level Monte-Carlo method for Uncertainty Quantification in Turbulent Compressible Aerodynamics Problems modeled by RANS

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

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Partitioned Algorithms for Fluid-Structure Interaction Problems in Haemodynamics

MATHICSE Technical Report : A quasi-optimal sparse grids procedure for groundwater flows

A Posteriori Error Estimation for the Stochastic Collocation Finite Element Method

MATHICSE Technical Report : Comparison of Clenshaw-Curtis and Leja quasi-optimal sparse grids for the approximation of random PDEs

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

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

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

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

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

Convergence analysis of Padé approximations for Helmholtz frequency response problems

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

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