Publications related to An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

MATHICSE Technical Report : An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

Fabio Nobile, Lorenzo Tamellini, Francesco Tesei

In this work we build on the classical adaptive sparse grid algorithm (T. Gerstner and M. Griebel, Dimension-adaptive tensor-product quadrature), obtaining an enhanced version capable of using non-nested collocation points, and supporting quadrature and in ...

MATHICSE2015

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

Fabio Nobile, Marco Picasso, Diane Sylvie Guignard

In this paper, 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 para ...

MATHICSE2014

MATHICSE Technical Report : 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. Moreover, we discuss extensions to non-unif ...

MATHICSE2014

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

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

Fabio Nobile, Eleonora Musharbash

In this work we discuss the Dynamically Orthogonal (DO) approximation of time dependent partial differential equations with random data. The approximate solution is expanded at each time instant on a time dependent orthonormal basis in the physical domain ...

MATHICSE2014

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Erik Gustaf Bogislaw Von Schwerin, Hakon Andreas Hoel

We consider the setting of estimating the mean of a random variable by a sequential stopping rule Monte Carlo (MC) method. The performance of a typical second moment based sequential stopping rule MC method is shown to be unreliable in such settings both b ...

Siam Publications2014

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

Interface control domain decomposition methods for heterogeneous problems

Alfio Quarteroni, Marco Discacciati

This paper is concerned with the solution of heterogeneous problems by the interface control domain decomposition (ICDD) method, a strategy introduced for the solution of partial differential equations in computational domains partitioned into subdomains t ...

Wiley-Blackwell2014

Shortest-Weight Paths In Random Regular Graphs

Léo Hamed Amini

Consider a random regular graph with degree d and of size n. Assign to each edge an independent and identically distributed exponential random variable with mean one. In this paper we establish a precise asymptotic expression for the maximum number of edge ...

Siam Publications2014

Accurate and efficient evaluation of failure probability for partial different equations with random input data

Alfio Quarteroni, Peng Chen

Several computational challenges arise when evaluating the failure probability of a given system in the context of risk prediction or reliability analysis. When the dimension of the uncertainties becomes high, well established direct numerical methods can ...

Elsevier Science Sa2013

An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data

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MATHICSE Technical Report : An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

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

Interface control domain decomposition methods for heterogeneous problems

Shortest-Weight Paths In Random Regular Graphs

Accurate and efficient evaluation of failure probability for partial different equations with random input data

MATHICSE Technical Report : An adaptive sparse grid algorithm for elliptic PDEs with lognormal diffusion coefficient

MATHICSE Technical Report : On the dynamically orthogonal approximation of time dependent random PDEs

MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties

On Nonasymptotic Optimal Stopping Criteria In Monte Carlo Simulations

Accurate and efficient evaluation of failure probability for partial different equations with random input data

MATHICSE Technical Report : Optimization of mesh hierarchies in multilevel Monte Carlo samplers

Perturbation analysis for the Darcy problem with log-normal permeability

Interface control domain decomposition methods for heterogeneous problems

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

Shortest-Weight Paths In Random Regular Graphs