Publications related to Asymptotics and analytic modes for the wave equation in similarity coordinates

Multiscale methods for wave problems in heterogenous media

In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogenous media. We concentrate on the wave equation and distinguish between two classes of applications. First we dis ...

2017

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 : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

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 vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

MATHICSE Technical Report : Multiscale methods for wave problems in heterogeneous media

Assyr Abdulle, Patrick Henning

In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogenous media. We concentrate on the wave equation and distinguish between two classes of applications. First we dis ...

MATHICSE2016

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

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

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

Hoài-Minh Nguyên

This paper concerns approximate cloaking by mapping for a full, but scalar wave equation, when one allows for physically relevant frequency dependence of the material properties of the cloak. The paper is a natural continuation of [20], but here we employ ...

Elsevier2016

Asymptotics and analytic modes for the wave equation in similarity coordinates

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Multiscale methods for wave problems in heterogenous media

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

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

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

A vector field method on the distorted Fourier side and decay for wave equations with potentials

MATHICSE Technical Report : Multiscale methods for wave problems 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

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Multiscale methods for wave problems in heterogenous media

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

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

A vector field method on the distorted Fourier side and decay for wave equations with potentials

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

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

MATHICSE Technical Report : Multiscale methods for wave problems in heterogeneous media

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

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