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

Incentive Schemes for Participatory Sensing

We consider a participatory sensing scenario where a group of private sensors observes the same phenomenon, such as air pollution. Since sensors need to be installed and maintained, owners of sensors are inclined to provide inaccurate or random data. We de ...

2015

Lyapunov exponents of random walks in small random potential: the upper bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on Z(d) evolving in a random i.i.d. potential taking values in [0, +infinity). The potential is not assumed integrable, and can be rescaled by a multiplicative factor lambda > 0. Completing the work started in a companion ...

Univ Washington, Dept Mathematics2015

Asynchronous Adaptation and Learning Over Networks—Part III: Comparison Analysis

Ali H. Sayed

In Part II of this paper, also in this issue, we carried out a detailed mean-square-error analysis of the performance of asynchronous adaptation and learning over networks under a fairly general model for asynchronous events including random topologies, ra ...

Institute of Electrical and Electronics Engineers2015

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 : 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

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 : 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

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

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

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we propose and analyze a weighted reduced basis method to solve elliptic partial differential equations (PDEs) with random input data. The PDEs are first transformed into a weighted parametric elliptic problem depending on a finite number of p ...

Siam Publications2013

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

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Incentive Schemes for Participatory Sensing

Lyapunov exponents of random walks in small random potential: the upper bound

Asynchronous Adaptation and Learning Over Networks—Part III: Comparison Analysis

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

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

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

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

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

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

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

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

Lyapunov exponents of random walks in small random potential: the upper bound

Incentive Schemes for Participatory Sensing

Asynchronous Adaptation and Learning Over Networks—Part III: Comparison Analysis

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

A Weighted Reduced Basis Method For Elliptic Partial Differential Equations With Random Input Data

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

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

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

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