Publications related to Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

Conservative Model Order Reduction for Fluid Flow

Qian Wang, Jan Sickmann Hesthaven, Nicolò Ripamonti, Babak Maboudi Afkham

In the past decade, model order reduction (MOR) has been successful in reducing the computational complexity of elliptic and parabolic systems of partial differential equations (PDEs). However, MOR of hyperbolic equations remains a challenge. Symmetries an ...

Springer Verlag2018

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

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

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

Elisabetta Chiodaroli

We consider the initial value problem for the inviscid Primitive and Boussinesq equations in three spatial dimensions. We recast both systems as an abstract Euler-type system and apply the methods of convex integration of De Lellis and Sz,kelyhidi to show ...

Springer Verlag2017

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

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

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

IGS: an IsoGeometric approach for Smoothing on surfaces

Pierre Wilhelm, Luca Dede', Matthieu Wilhelm

We propose a novel approach for smoothing on surfaces. More precisely, we aim at estimating functions lying on a surface, starting from noisy and discrete measurements. The surface is represented by NURBS, which are geometrical representations commonly use ...

Elsevier2016

Particle-size and -density segregation in granular free-surface flows

Christophe Ancey

When a mixture of particles, which differ in both their size and their density, avalanches downslope, the grains can either segregate into layers or remain mixed, dependent on the balance between particle-size and particle-density segregation. In this pape ...

2015

Ill-posedness of the quasilinear wave equation in the space $H^7/4 (ln H)^-Béta$ in dimension 2+1

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Conservative Model Order Reduction for Fluid Flow

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

Dynamical Low Rank approximation of PDEs with random parameters

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

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

Multiscale methods for wave problems in heterogenous 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

IGS: an IsoGeometric approach for Smoothing on surfaces

Particle-size and -density segregation in granular free-surface flows

Conservative Model Order Reduction for Fluid Flow

Dynamical Low Rank approximation of PDEs with random parameters

IGS: an IsoGeometric approach for Smoothing on surfaces

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

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

Existence and Non-uniqueness of Global Weak Solutions to Inviscid Primitive and Boussinesq Equations

Multiscale methods for wave problems in heterogenous media

Particle-size and -density segregation in granular free-surface flows

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

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