Publications related to Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Perturbation analysis for the Darcy problem with log-normal permeability

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

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

Yun Bai

The characteristic of effective properties of physical processes in heterogeneous media is a basic modeling and computational problem for many applications. As standard numerical discretization of such multiscale problems (e.g. with classical finite elemen ...

EPFL2013

Refractive Index Sensing with Subradiant Modes: A Framework To Reduce Losses in Plasmonic Nanostructures

Olivier Martin, Benjamin Gallinet

Plasmonic modes with long radiative lifetimes, subradiant modes, combine strong confinement of the electromagnetic energy at the nanoscale with a steep spectral dispersion, which makes them promising for biochemical sensors or immunoassays. Subradiant mode ...

2013

MATHICSE Technical Report : 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 ...

MATHICSE2013

MATHICSE Technical Report : Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

Fabio Nobile, Annalisa Buffa, Francesca Bonizzoni

We study the mixed formulation of the stochastic Hodge-Laplace problem defined on a n-dimensional domain D (

n \geq 1

), with random forcing term. In particular, we focus on the magnetostatic problem and on the Darcy problem in the three dimensional case. ...

MATHICSE2012

Numerical Integration of SDEs: A Short Tutorial

Thomas Schaffter

Introduction to numerical methods to simulate systems of stochastic differential equations (SDEs) both in Ito and Stratonovich scheme. ...

2010

Stationary and time-dependent correlations in polariton condensates

Paolo Schwendimann, Antonio Quattropani, Davide Sarchi

The statistics of the condensed polaritons is described in terms of the Wigner function. In the framework of the truncated Wigner method, the Wigner function obeys a Fokker-Planck equation, which is solved analytically. The second-order correlations in the ...

2010

Optimization Problem Coupled with Differential Equations: A Numerical Algorithm Mixing an Interior-Point Method and Event Detection

Jacques Rappaz, Alexandre Caboussat, Christian Landry

The numerical analysis of a dynamic constrained optimization problem is presented. It consists of a global minimization problem that is coupled with a system of ordinary differential equations. The activation and the deactivation of inequality constraints ...

2010

Hybrid Numerical Solution of the Chemical Master Equation

Maria-Emanuela-Canini Mateescu, Verena Wolf

We present a numerical approximation technique for the analysis of continuous-time Markov chains that describe networks of biochemical reactions and play an important role in the stochastic modeling of biological systems. Our approach is based on the const ...

2010

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Fabio Nobile

We consider the problem of numerically approximating statistical moments of the solution of a time-dependent linear parabolic partial differential equation (PDE), whose coefficients and/or forcing terms are spatially correlated random fields. The stochasti ...

2009

Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Graph Chatbot

Chat with Graph Search

Perturbation analysis for the Darcy problem with log-normal permeability

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

Refractive Index Sensing with Subradiant Modes: A Framework To Reduce Losses in Plasmonic Nanostructures

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

Numerical Integration of SDEs: A Short Tutorial

Stationary and time-dependent correlations in polariton condensates

Optimization Problem Coupled with Differential Equations: A Numerical Algorithm Mixing an Interior-Point Method and Event Detection

Hybrid Numerical Solution of the Chemical Master Equation

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Optimization Problem Coupled with Differential Equations: A Numerical Algorithm Mixing an Interior-Point Method and Event Detection

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

MATHICSE Technical Report : Moment equations for the mixed formulation of the Hodge Laplacian with stochastic data

Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients

Reduced order modeling techniques for numerical homogenization methods applied to linear and nonlinear multiscale problems

Numerical Integration of SDEs: A Short Tutorial

Refractive Index Sensing with Subradiant Modes: A Framework To Reduce Losses in Plasmonic Nanostructures

Perturbation analysis for the Darcy problem with log-normal permeability

Stationary and time-dependent correlations in polariton condensates

Hybrid Numerical Solution of the Chemical Master Equation