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We consider the scattering of time-dependent acoustic waves by some bounded obstacles located in a homogeneous and non-dissipative medium. We propose a far-field model of time reversal mirror that reverses the asymptotic wave profile of a scattered wave. Following the idea developed for time-harmonic waves in the so-called decomposition of the time reversal operator in French (DORT) method, we define a time reversal operator (TRO) in the time domain, which is related to the scattering operator involved in scattering theory. We show how this operator is related to the family of single frequency TROs involved in the DORT method, which clarifies the link between time-dependent and time-harmonic waves in the time reversal process. As an application of this relation, we prove that iterative time reversal generally converges to a single frequency time-harmonic wave. [ABSTRACT FROM PUBLISHER]

This paper explores from the point of view of numerical analysis a method for solving the acoustic time-harmonic wave equation in a locally non-uniform 2D waveguide. The multimodal method is based on a spectral description of the acoustic field in each transverse section of the guide, using Fourier-like series. In the case of sound-hard boundaries, the weak point of the method lies in the poor convergence of such series due to a poor approximation of the field near the boundaries. A remedy was proposed by Athanassoulis & Belibassakis (1999, J. Fluid Mech., 389, 275–301), where the convergence is improved thanks to the use of enhanced series. The present paper proposes a theoretical analysis of their idea and studies further improvements. For a general model which includes different kinds of non-uniformity (varying cross section, bend and inhomogeneous medium), a hybrid spectral/variational formulation is introduced. Error estimates are provided for a semi-discretized problem which concerns the effect of spectral truncation. These estimates are confirmed by numerical results. [ABSTRACT FROM PUBLISHER]

We study the time reversal phenomenon in a homogeneous and nondissipative medium containing sound-hard obstacles. We propose two mathematical models of time reversal mirrors in the frequency domain. The first one takes into account the interactions between the mirror and the obstacles. The second one provides an approximation of these interactions. We prove, in both cases, that the time reversal operator T is self-adjoint and compact. The DORT method (French acronym for decomposition of the time reversal operator) is explored numerically. In particular, we show that selective focusing, which is known to occur for small and distant enough scatterers, holds when the wavelength and the size of these scatterers are of the same order of magnitude (medium frequency situation). Moreover, we present the behavior of the eigenvalues of T according to the frequency, and we show their oscillations due to the interactions between the mirror and the obstacles and between the obstacles themselves. [ABSTRACT FROM AUTHOR]