The Kirchhoff approximation is widely used to describe the scatter of elastodynamic waves. It simulates the scattered field as the convolution of the free-space Green’s tensor with the geometrical elastodynamics approximation to the total field on the scatterer surface and, therefore, cannot be used to describe nongeometrical phenomena, such as head waves. The aim of this paper is to demonstrate that an alternative approximation, the convolution of the far-field asymptotics of the Lamb’s Green’s tensor with incident surface tractions, has no such limitation. This is done by simulating the scatter of a critical Gaussian beam of transverse motions from an infinite plane. The results are of interest in ultrasonic nondestructive testing.

Consider the time-harmonic acoustic scattering from an extended elastic body surrounded by a finite number of point-like obstacles in a fluid. We assume point source waves are emitted from arrayed transducers and the signals of scattered near-field data are recorded by receivers not far away from the scatterers (compared to the incident wavelength). The forward scattering can be modeled as an interaction problem between acoustic and elastic waves together with a multiple scattering problem between the extend solid and point scatterers. We prove a necessary and sufficient condition that can be used simultaneously to recover the shape of the extended elastic solid and to locate the positions of point scatterers. The essential ingredient in our analysis is the outgoing-to-incoming (OtI) operator applied to the resulting near-field response matrix (or operator). In the first part, we justify the MUSIC algorithm for locating point scatterers from near-field measurements. In the second part, we apply the factorization method, the continuous analogue of MUSIC, to the two-scale scattering problem for determining both extended and point scatterers. Numerical examples in 2D are demonstrated to show the validity and accuracy of our inversion algorithms.

The purpose of this paper is to numerically realize the inverse scattering scheme proposed in [19] of reconstructing complex elastic objects by a single far-field measurement. The unknown elastic scatterers might consist of both rigid bodies and traction-free cavities with components of multiscale sizes presented simultaneously. We conduct extensive numerical experiments to show the effectiveness and efficiency of the imaging scheme proposed in [19]. Moreover, we develop a two-stage technique, which can significantly speed up the reconstruction to yield a fast imaging scheme.

The coordinate transformation offers a remarkable way to design cloaks that can steer electromagnetic fields so as to prevent waves from penetrating into the cloaked region (denoted by Ω0, where the objects inside are invisible to observers outside). The ideal circular and elliptic cylindrical cloaked regions are blown up from a point and a line segment, respectively so the transformed material parameters and the corresponding coefficients of the resulted equations are highly singular at the cloaking boundary ∂Ω0. The electric field or magnetic field is not continuous across ∂Ω0. The imposition of appropriate cloaking boundary conditions (CBCs) to achieve perfect concealment is a crucial but challenging issue.

Based upon the principle that a well-behaved electromagnetic field in the original space must be well-behaved in the transformed space as well, we obtain CBCs that intrinsically relate to the essential “pole” conditions of a singular transformation. We also find that for the elliptic cylindrical cloak, the CBCs should be imposed differently for the cosine-elliptic and sine-elliptic components of the decomposed fields. With these at our disposal, we can rigorously show that the governing equation in Ω0 can be decoupled from the exterior region , and the total fields in the cloaked region vanish under mild conditions. We emphasize that our proposal of CBCs is different from any existing ones.

Using the exact circular (resp., elliptic) Dirichlet-to-Neumann (DtN) non-reflecting boundary conditions to reduce the unbounded domain to a bounded domain, we introduce an accurate and efficient Fourier-Legendre spectral-element method (FLSEM) (resp., Mathieu-Legendre spectral-element method (MLSEM)) to simulate the circular cylindrical cloak (resp., elliptic cylindrical cloak). We provide ample numerical results to demonstrate that the perfect concealment of waves can be achieved for the ideal circular/elliptic cylindrical cloaks under our proposed CBCs and accurate numerical solvers.

This paper considers the effect of a hard-wall beach on the downstream side of submerged parallel bars in a breakwater. In previous research, it was assumed that the beach can absorb all of the transmitted wave energy, when an optimal dimension for a submerged parallel bar is obtained and the wave amplitude is reduced as more bars are installed. However, for a hard-wall beach there are waves reflected from the beach that change the long-term wave interaction. We adopt the linear shallow water equations in Riemann invariant form and use the method of characteristics, in a procedure applicable to various formations of submerged rectangular bars. The distance from the parallel bar (or bars) to the beach determines the phase differences between right running waves in the beach basin and whether they superpose destructively or constructively before hitting the beach, to define the safest and the most dangerous cases. Our numerical calculations for one bar, two bars and for periodic rectangular bars confirm the analytical formulae obtained.

An isolated cylindrical void is located inside an incompressible nonlinear-elastic medium whose constitutive behaviour is governed by a neo-Hookean strain energy function. In-plane hydrostatic pressure is applied in the far-field so that the void changes its radius and an inhomogeneous region of deformation arises in the vicinity of the void. We consider scattering from the void in the deformed configuration due to an incident field (of small amplitude) generated by a horizontally polarized shear (SH) line source, a distance r0 (R0) away from the centre of the void in the deformed (undeformed) configuration. We show that the scattering coefficients of this scattered field are unaffected by the pre-stress (initial deformation). In particular, they depend not on the deformed void radius a or distance r0, but instead on the original void size A and original distance R0.

We propose a numerical procedure to extend to full aperture the acoustic far-field pattern (FFP) when measured in only few observation angles. The reconstruction procedure is a multi-step technique that combines a total variation regularized iterative method with the standard Tikhonov regularized pseudo-inversion. The proposed approach distinguishes itself from existing solution methodologies by using an exact representation of the total variation which is crucial for the stability and robustness of Newton algorithms. We present numerical results in the case of two-dimensional acoustic scattering problems to illustrate the potential of the proposed procedure for reconstructing the full aperture of the FFP from very few noisy data such as backscattering synthetic measurements.

This work concerns multiple-scattering problems for time-harmonic equations in a reference generic media. We consider scatterers that can be sources, obstacles or compact perturbations of the reference media. Our aim is to restrict the computational domain to small compact domains containing the scatterers. We use Robin-to-Robin (RtR) operators (in the most general case) to express boundary conditions for the interior problem. We show that one can always factorize the RtR map using only operators defined using single-scatterer problems. This factorization is based on a decomposition of the diffracted field, on the whole domain where it is defined. Assuming that there exists a good method for solving single-scatterer problems, it then gives a convenient way to compute RtR maps for a random number of scatterers.

The analysis of seismic wave propagation and amplification in complex geological structures requires efficient numerical methods. In this article, following up on recent studies devoted to the formulation, implementation and evaluation of 3-D single- and multi-region elastodynamic fast multipole boundary element methods (FM-BEMs), a simple preconditioning strategy is proposed. Its efficiency is demonstrated on both the single- and multi-region versions using benchmark examples (scattering of plane waves by canyons and basins). Finally, the preconditioned FM-BEM is applied to the scattering of plane seismic waves in an actual configuration (alpine basin of Grenoble, France), for which the high velocity contrast is seen to significantly affect the overall efficiency of the multi-region FM-BEM.

Jakeman's random walk model with step number fluctuations describes the coherent amplitude scattered from a rough medium in terms of the summation of individual scatterers' contributions. If the scattering population conforms to a birth-death immigration model, the resulting amplitude is K-distributed. In this context, we derive a class of diffusion processes as an extension of the ordinary birth-death immigration model. We show how this class encompasses four different cross-section models commonly studied in the literature. We conclude by discussing the advantages of this unified description.