Publications related to Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

Isogeometric Analysis of Electrophysiological Models on Surfaces

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

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Benoit Till Cretegny

Identification of kinetic models and estimation of reaction and mass-transfer parameters can be performed using the extent-based identification method, whereby each chemical/physical process is treated individually. This method is used here to analyze gas- ...

2013

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan, Benoit Till Cretegny

Identification of kinetic models and estimation of reaction and mass-transfer parameters can be performed using the extent-based identification method, whereby each chemical/physical process is handled separately [1-3]. This method is used here to analyze ...

2013

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

Dominique Bonvin, Julien Léo Billeter, Sriniketh Srinivasan

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

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Assyr Abdulle, Gilles Vilmart

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by t ...

Elsevier2013

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Gilles Brunner

In this project, we study and compare two methods to solve stochastic ordinary differential equations. The first is the Monte Carlo method and the second uses Polynomial Chaos. In the first part, we will solve a stochastic ordinary differential equation by ...

2013

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Le Chen

In this thesis, we study several stochastic partial differential equations (SPDE’s) in the spatial domain R, driven by multiplicative space-time white noise. We are interested in how rough and unbounded initial data affect the random field solution and the ...

EPFL2013

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Michaël Unser, Emrah Bostan, Ulugbek Kamilov, Masih Nilchian

We present a novel statistically-based discretization paradigm and derive a class of maximum a posteriori (MAP) estimators for solving ill-conditioned linear inverse problems. We are guided by the theory of sparse stochastic processes, which specifies cont ...

Ieee-Inst Electrical Electronics Engineers Inc2013

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Assyr Abdulle, Gilles Vilmart

We introduce two drift-diagonally-implicit and derivative-free integrators for stiff systems of It stochastic differential equations with general non-commutative noise which have weak order 2 and deterministic order 2, 3, respectively. The methods are show ...

2013

Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty

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Isogeometric Analysis of Electrophysiological Models on Surfaces

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

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

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Moments, Intermittency, and Growth Indices for Nonlinear Stochastic PDE's with Rough Initial Conditions

Solving Stochastic Ordinary Differential Equations by Monte Carlo and Polynomial Chaos

Sparse Stochastic Processes and Discretization of Linear Inverse Problems

Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations

Isogeometric Analysis of Electrophysiological Models on Surfaces

Incremental Model Identification of Gas-Liquid Reaction Systems with Unsteady-State Diffusion

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

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

PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise