Displaying similar documents to “Sweeping preconditioners for elastic wave propagation with spectral element methods”

Long-Wave Coupled Marangoni - Rayleigh Instability in a Binary Liquid Layer in the Presence of the Soret Effect

A. Podolny, A. A. Nepomnyashchy, A. Oron (2008)

Mathematical Modelling of Natural Phenomena

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We have explored the combined long-wave Marangoni and Rayleigh instability of the quiescent state of a binary- liquid layer heated from below or from above in the presence of the Soret effect. We found that in the case of small Biot numbers there are two long- wave regions of interest ~ and ~ . The dependence of both monotonic and oscillatory thresholds of instability in these regions on both the Soret and dynamic Bond numbers has been investigated....

Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators

S. A. Denisov (2010)

Mathematical Modelling of Natural Phenomena

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In this paper, we consider one-dimensional wave equation with real-valued square-summable potential. We establish the long-time asymptotics of solutions by, first, studying the stationary problem and, second, using the spectral representation for the evolution equation. In particular, we prove that part of the wave travels ballistically if ∈ (ℝ) and this result is sharp.

T-coercivity for scalar interface problems between dielectrics and metamaterials

Anne-Sophie Bonnet-Ben Dhia, Lucas Chesnel, Patrick Ciarlet (2012)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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Some electromagnetic materials have, in a given frequency range, an effective dielectric permittivity and/or a magnetic permeability which are real-valued negative coefficients when dissipation is neglected. They are usually called metamaterials. We study a scalar transmission problem between a classical dielectric material and a metamaterial, set in an open, bounded subset of R, with  = 23. Our aim is to characterize occurences where the problem is well-posed within the Fredholm (or...

A uniformly controllable and implicit scheme for the 1-D wave equation

Arnaud Münch (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper studies the exact controllability of a finite dimensional system obtained by discretizing in space and time the linear 1-D wave system with a boundary control at one extreme. It is known that usual schemes obtained with finite difference or finite element methods are not uniformly controllable with respect to the discretization parameters and Δ. We introduce an implicit finite difference scheme which differs from the usual centered one by additional terms of order ...