Publications related to Dynamical Low Rank approximation of PDEs with random parameters

A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks

Alfio Quarteroni, Gianluigi Rozza, Laura Iapichino

In this paper we propose a reduced basis hybrid method (RBHM) for the approximation of partial differential equations in domains represented by complex networks where topological features are recurrent. The RBHM is applied to Stokes equations in domains wh ...

Elsevier2012

High weak order methods for stochastic equations based on modified equations

Assyr Abdulle, Gilles Vilmart, David Cohen

Inspired by recent advances in the theory of modified differential equations, we propose a new methodology for constructing numerical integrators with high weak order for the time integration of stochastic differential equations. This approach is illustrat ...

Siam Publications2012

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Laura Vinckenbosch

The topic of this thesis is the study of several stochastic control problems motivated by sailing races. The goal is to minimize the travel time between two locations, by selecting the fastest route in face of randomly changing weather conditions, such as ...

EPFL2012

Markov chains with discontinuous drifts have differential inclusion limits

Nicolas Gabriel Gast

In this paper, we study deterministic limits of Markov processes having discontinuous drifts. While most results assume that the limiting dynamics is continuous, we show that these conditions are not necessary to prove convergence to a deterministic system ...

Elsevier2012

Convergence Analysis For Spectral Approximation To A Scalar Transport Equation With A Random Wave Speed

This paper is concerned with the initial-boundary value problems of scalar transport equations with uncertain transport velocities. It was demonstrated in our earlier works that regularity of the exact solutions in the random spaces (or the parametric spac ...

Vsp Bv2012

MATHICSE Technical Report : 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 coeffcients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solu ...

MATHICSE2012

Reduced Variational Formulations in Free Boundary Continuum Mechanics

Tudor Ratiu, François Gay-Balmaz

We present the material, spatial, and convective representations for elasticity and fluids with a free boundary from the Lagrangian reduction point of view, using the material and spatial symmetries of these systems. The associated constrained variational ...

Springer-Verlag2012

The Bounded Confidence Model Of Opinion Dynamics

Jean-Yves Le Boudec, Javier Gomez Serrano

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into ...

World Scientific Publishing2012

A class of Neumann type systems and its application

Jinbing Chen

A class of Neumann type systems are derived separating the spatial and temporal variables for the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation and the modified Korteweg-de Vries (mKdV) hierarchy. The Lax-Moser matrix of Neumann type s ...

International Press2012

Full range of blow up exponents for the quintic wave equation in three dimensions

Joachim Krieger

For the critical focusing wave equation

\square u=u^5

on

\mathbb{R}^{3+1}

in the radial case, we prove the existence of type II blow up solutions with scaling parameter

\lambda(t)=t^{-1\nu}

for all

\nu>0

. This extends the previous work by the autho ...

Elsevier2012

Dynamical Low Rank approximation of PDEs with random parameters

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A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks

High weak order methods for stochastic equations based on modified equations

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Markov chains with discontinuous drifts have differential inclusion limits

Convergence Analysis For Spectral Approximation To A Scalar Transport Equation With A Random Wave Speed

MATHICSE Technical Report : Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients

Reduced Variational Formulations in Free Boundary Continuum Mechanics

The Bounded Confidence Model Of Opinion Dynamics

A class of Neumann type systems and its application

Full range of blow up exponents for the quintic wave equation in three dimensions

Reduced Variational Formulations in Free Boundary Continuum Mechanics

Convergence Analysis For Spectral Approximation To A Scalar Transport Equation With A Random Wave Speed

A reduced basis hybrid method for the coupling of parametrized domains represented by fluidic networks

Markov chains with discontinuous drifts have differential inclusion limits

A class of Neumann type systems and its application

MATHICSE Technical Report : Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients

The Bounded Confidence Model Of Opinion Dynamics

Stochastic Control and Free Boundary Problems for Sailboat Trajectory Optimization

Full range of blow up exponents for the quintic wave equation in three dimensions

High weak order methods for stochastic equations based on modified equations