Publications related to Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

A fully discrete analysis of the finite element heterogeneous multiscale method for a class of nonlinear elliptic homogenization problems of nonmonotone type is proposed. In contrast to previous results obtained for such problems in dimension

d\leq2

for ...

Amer Mathematical Soc2014

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

Antoine Giovanni Imboden

In this report, we first introduce operator splitting as a way to solve nonlinear reaction-diffusion PDEs. We then present a flux-limiting technique for anisotropic diffusion problems that allows to recover the discrete maximum principle. Finally, we imple ...

2014

Solving the infinite-horizon constrained LQR problem using splitting techniques

Colin Neil Jones, Milan Korda, Georgios Stathopoulos

This paper presents a method to solve the constrained infinite-time linear quadratic regulator (LQR) problem. We use an operator splitting technique, namely the alternating minimization algorithm (AMA), to split the problem into an unconstrained LQR proble ...

2014

Solving the infinite-horizon constrained LQR problem using splitting techniques

Colin Neil Jones, Milan Korda, Georgios Stathopoulos

This paper presents a method to solve the constrained infinite-time linear quadratic regulator (LQR) problem. We use an operator splitting technique, namely the alternating minimization algorithm (AMA), to split the problem into an unconstrained LQR proble ...

Elsevier2014

BPX-preconditioning for isogeometric analysis

Annalisa Buffa

We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by ...

2013

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

The Adomian Decomposition Method for Nonlinear Partial Differential Equations

Natalie Sauerwald

The goal of this report is to study the method introduced by Adomian known as the Adomian Decomposition Method (ADM), which is used to find an approximate solution to nonlinear partial differential equations (PDEs) as a series expansion involving the recur ...

2013

Numerical methods for stochastic partial differential equations with multiple scales

Assyr Abdulle, Grigorios A. Pavliotis

A new method for solving numerically stochastic partial differential equations (SPDEs) with multiple scales is presented. The method combines a spectral method with the heterogeneous multiscale method (HMM) presented in [W. E, D. Liu, E. Vanden-Eijnden, An ...

2012

Numerical pancake droplets: from capturing to versatile microfluidics

François Gallaire, Mathias Nagel

This article proposes a numerical model for microfluidic two-phase flows in flat channels, also called Hele-Shaw cells. The initially three-dimensional problem is simplified to two-dimensions by depth averaging in the thin direction. The 2D partial differe ...

SOCIETE HYDROTECHNIQUE DE FRANCE2012

Fully discrete heterogeneous Multiscale methods and application to transport problems in microarrays

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Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

Solving the infinite-horizon constrained LQR problem using splitting techniques

Solving the infinite-horizon constrained LQR problem using splitting techniques

BPX-preconditioning for isogeometric analysis

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

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

The Adomian Decomposition Method for Nonlinear Partial Differential Equations

Numerical methods for stochastic partial differential equations with multiple scales

Numerical pancake droplets: from capturing to versatile microfluidics

Numerical methods for nonlinear reaction-diffusion equations with traveling wave solutions

The Adomian Decomposition Method for Nonlinear Partial Differential Equations

Analysis of the finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems

BPX-preconditioning for isogeometric analysis

Numerical methods for stochastic partial differential equations with multiple scales

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

Solving the infinite-horizon constrained LQR problem using splitting techniques

Solving the infinite-horizon constrained LQR problem using splitting techniques

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

Numerical pancake droplets: from capturing to versatile microfluidics