Publications by Timothée Noé Pouchon

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

A family of effective equations for wave propagation in periodic media for arbitrary timescales O(epsilon-alpha), where epsilon MUCH LESS-THAN1 is the period of the tensor describing the medium, is proposed. The well-posedness of the effective equations of ...

SPRINGER2020

Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media

Timothée Noé Pouchon

Modeling wave propagation in highly heterogeneous media is of prime importance in engineering applications of diverse nature such as seismic inversion, medical imaging or the design of composite materials. The numerical approximation of such multiscale phy ...

EPFL2017

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for the wave equation in locally periodic media over long time is derived. In particular, explicit formulas for the effective tensors are provided. To validate the derivation, an a priori error estimate between the effective ...

MATHICSE2017

A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time

Timothée Noé Pouchon, Assyr Abdulle

A fully discrete a priori analysis of the finite element heterogeneous multiscale method introduced in [A. Abdulle, M. Grote, and C. Stohrer, Multiscale Model. Simul., 12, 2014, pp. 1135-1166] for the wave equation with highly oscillatory coefficients over ...

Siam Publications2016

Integrated stochastic modeling of pharmaceuticals in sewage networks

Sylvain Coutu, Timothée Noé Pouchon, Pierre Claude Jean Queloz

Pharmaceuticals and particularly antibiotics can harm sensitive aquatic species. Their occurrence in urban wastewater systems is the consequence of five successive processes: (i) ingestion of the substance, (ii) accumulation in the urine, (iii) excretion, ...

Springer Verlag2016

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain Omega subset of R-d is proposed and analyzed. For a wave equation with highly oscillatory ...

World Scientific Publ Co Pte Ltd2016

MATHICSE Technical Report : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations that capture the long time dispersive effects of wave propagation in heterogeneous media in an arbitrary large periodic spatial domain

\Omega \subset \mathbb{R}^d

over long time is proposed and analyzed. For a wave equatio ...

MATHICSE2016

MATHICSE Technical Report : A priori error analysis of the finite element heterogenenous multiscale method for the wave equation in heterogenenous media over long time

Timothée Noé Pouchon

A fully discrete a priori analysis of the finite element heterogenenous multiscale method (FE-HMM) introduced in [A. Abdulle, M. Grote, C. Stohrer, MultiscaleModel. Simul. 2014] for the wave equation with highly oscillatory coefficients over long time is p ...

MATHICSE2015

A computational platform for integrated modelling of micropollution in the urban environment

David Andrew Barry, Luca Rossi, Sylvain Coutu, Timothée Noé Pouchon

Anthropogenic chemical contaminants are found routinely in our water resources. Although most of these compounds are usually present at low concentrations, they are of concern due to their ecotoxicity, antibacterial resistance and potential harm to human h ...

2013

Estimateur à posteriori pour l’affinage de maillage dans la méthode des éléments finis

Timothée Noé Pouchon

Dans ce travail, nous introduisons le concept d’estimateur à posteriori et la façon de l’utiliser pour affiner un maillage dans le cadre de la méthode des éléments finis. Dans la première partie, nous traitons le problème de Poisson, avec conditions de bord de Dirichlet homogènes et mixtes. Nous faisons la discrétisation avec la méthode de Galerkin et l’analysons. Puis, une analyse à posteriori est faite et nous donnons deux exemples numériques pour tester l’estimateur dans un affinage de maillage. La deuxième partie traite du problème de Stokes. Nous faisons une brève analyse du point de vue de la méthode des éléments finis, puis analysons une méthode stabilisée. Nous faisons ensuite l’analyse à posteriori de celle-ci et la testons ainsi que l’estimateur donné dans les exemples numériques.

2010

Timothée Noé Pouchon

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Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time

Integrated stochastic modeling of pharmaceuticals in sewage networks

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

MATHICSE Technical Report : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

MATHICSE Technical Report : A priori error analysis of the finite element heterogenenous multiscale method for the wave equation in heterogenenous media over long time

A computational platform for integrated modelling of micropollution in the urban environment

Estimateur à posteriori pour l’affinage de maillage dans la méthode des éléments finis

Effective Models and Numerical Homogenization for Wave Propagation in Heterogeneous Media on Arbitrary Timescales

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

Integrated stochastic modeling of pharmaceuticals in sewage networks

Effective models and numerical homogenization methods for long time wave propagation in heterogeneous media

A priori error analysis of the finite element heterogeneous multiscale method for the wave equation in heterogeneous media over long time

MATHICSE Technical Report : Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

Effective models for the multidimensional wave equation in heterogeneous media over long time and numerical homogenization

A computational platform for integrated modelling of micropollution in the urban environment

Estimateur à posteriori pour l’affinage de maillage dans la méthode des éléments finis

MATHICSE Technical Report : A priori error analysis of the finite element heterogenenous multiscale method for the wave equation in heterogenenous media over long time