Publication

Time and space adaptivity of the wave equation discretized in time by a second-order scheme

Related publications (42)

On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on

\mathbb{R}^{3+1}

constructed in [28], [27] are stable along a co-dimension three manifold of radial data perturbations in a suit ...

2018

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Jean-Philippe Lucien Montillet

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...

Int Center Scientific Research & Studies2017

Multiscale methods for wave problems in heterogenous 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 ...

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

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

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

2S

dynamica ...

2017

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 : 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

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On stability of type II blow up for the critical NLW on $\mathbb{R}^{3+1}$

Joachim Krieger

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on

\mathbb{R}^{3+1}

constructed in [28], [27] are stable along a co-dimension three manifold of radial data perturbations in a suit ...

2018

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 : 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

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

2S

dynamica ...

2017