Publications related to Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a ...

MATHICSE2015

A continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models. The CMLMC algorithm solves the given approximation problem for a sequence of decreasing tolerances, ending when the required error tolera ...

2015

Analysis and Computation of Hyperbolic PDEs with Random Data

Fabio Nobile

Hyperbolic partial differential equations (PDEs) are mathematical models of wave phenomena, with applications in a wide range of scientific and engineering fields such as electromagnetic radiation, geosciences, fluid and solid mechanics, aeroacoustics, and ...

2015

Incentive Schemes for Participatory Sensing

Boi Faltings, Goran Radanovic

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

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

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 continuation multilevel Monte Carlo algorithm

Fabio Nobile, Erik Gustaf Bogislaw Von Schwerin

We propose a novel Continuation Multi Level Monte Carlo (CMLMC) algorithm for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The CMLMC algorithm so ...

MATHICSE2014

Isogeometric Analysis of Electrophysiological Models on Surfaces

Alessandro Samuele Patelli

In this project we numerically simulate electrophysiological models for cardiac applications by means of Isogeometric Analysis. Specifically, we aim at understanding the advantages of using high order continuous NURBS (Non-UniformRational B-Splines) basis ...

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

Error Analysis of the Dynamically Orthogonal Approximation of Time Dependent Random PDEs

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MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

A continuation multilevel Monte Carlo algorithm

Analysis and Computation of Hyperbolic PDEs with Random Data

Incentive Schemes for Participatory Sensing

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

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

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

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Isogeometric Analysis of Electrophysiological Models on Surfaces

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

A continuation multilevel Monte Carlo algorithm

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

Analysis and Computation of Hyperbolic PDEs with Random Data

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

Isogeometric Analysis of Electrophysiological Models on Surfaces

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

Incentive Schemes for Participatory Sensing

MATHICSE Technical Report : Multi-index stochastic collocation convergence rates for random PDEs with parametric regularity

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