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

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

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

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

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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

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Fabio Nobile, Daniel Kressner, Christine Tobler, Rajesh Kumar

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 ...

MATHICSE2014

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Jean-Christophe Mourrat

The article begins with a quantitative version of the martingale central limit theorem, in terms of the Kantorovich distance. This result is then used in the study of the homogenization of discrete parabolic equations with random i.i.d. coefficients. For s ...

Springer Heidelberg2014

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

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

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The identification of kinetic models is an important step for the monitoring, control and optimization of industrial processes. This is particularly the case for highly competitive business sectors such as chemical and pharmaceutical industries, where the ...

2013

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

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MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

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

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

Interface control domain decomposition methods for heterogeneous problems

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations 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

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

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

MATHICSE Technical Report : A continuation multilevel Monte Carlo algorithm

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

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

MATHICSE Technical Report : Low-rank tensor approximation for high-order correlation functions of Gaussian random fields

Interface control domain decomposition methods for heterogeneous problems

Kantorovich distance in the martingale CLT and quantitative homogenization of parabolic equations with random coefficients

Incremental Model Identification of Fluid-Fluid Reaction Systems – Dynamic Accumulation and Reactions in the Diffusion Layer

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