Publications related to One-way wave equation

Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

Michaël Unser, Thanh-An Michel Pham, Emmanuel Emilien Louis Soubies

Optical diffraction tomography relies on solving an inverse scattering problem governed by the wave equation. Classical reconstruction algorithms are based on linear approximations of the forward model (Born or Rytov), which limits their applicability to t ...

2017

Localized orthogonal decomposition method for the wave equation with a continuum of scales

Assyr Abdulle, Patrick Henning

In this paper we propose and analyze a new multiscale method for the wave equation. The proposed method does not require any assumptions on space regularity or scale-separation and it is formulated in the framework of the Localized Orthogonal Decomposition ...

American Mathematical Society2017

Assessment of the Influence of Losses on the Performance of the Electromagnetic Time Reversal Fault Location Method

Mario Paolone, Reza Razzaghi, Gaspard Lugrin

Electromagnetic time reversal (EMTR) has been shown to be an efficient method for locating faults in AC and DC power grids. In the available literature, the back-propagation medium has been considered to have identical losses as the direct-time medium. How ...

Institute of Electrical and Electronics Engineers2017

Isogeometric Analysis And Proper Orthogonal Decomposition For The Acoustic Wave Equation

Alfio Quarteroni, Shengfeng Zhu

Discretization methods such as finite differences or finite elements were usually employed to provide high fidelity solution approximations for reduced order modeling of parameterized partial differential equations. In this paper, a novel discretization te ...

Edp Sciences S A2017

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

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

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

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

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

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

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Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

Localized orthogonal decomposition method for the wave equation with a continuum of scales

Assessment of the Influence of Losses on the Performance of the Electromagnetic Time Reversal Fault Location Method

Isogeometric Analysis And Proper Orthogonal Decomposition For The Acoustic Wave Equation

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

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

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

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

IGS: an IsoGeometric approach for Smoothing on surfaces

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

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

Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography

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

Localized orthogonal decomposition method for the wave equation with a continuum of scales

Assessment of the Influence of Losses on the Performance of the Electromagnetic Time Reversal Fault Location Method

Isogeometric Analysis And Proper Orthogonal Decomposition For The Acoustic Wave Equation

IGS: an IsoGeometric approach for Smoothing on surfaces

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