Towards a combined perfectly matching layer and infinite element formulation for unbounded elastic wave problems

This paper presents a framework for implementing a novel perfectly matching layer and infinite element (PML+IE) combination boundary condition for unbounded elastic wave problems in the time domain. To achieve this, traditional hexahedral finite elements are used to model wave propagation in the inner domain and IE test functions are implemented in the exterior domain. Two alternative implementations of the PML formulation are studied: the case with constant stretching in all three dimensions and the case with spatially dependent stretching along a single direction. The absorbing ability of the PML+IE formulation is demonstrated by the favourable comparison with the reflection coefficient for a plane wave incident on the boundary achieved using a finite-element-only approach where stress free boundary conditions are implemented at the domain edge. Values for the PML stretching function parameters are selected based on the minimisation of the reflected wave amplitude and it is shown that the same reduction in reflection amplitude can be achieved using the PML+IE approach with approximately half of the number of elements required in the finite-element-only approach.

Reflection of inhomogeneous plane waves at the surface of a thermo-poroelastic medium

SUMMARY We analyse the reflection coefficient of an inhomogeneous plane wave incident on the thermally insulated surface of a thermo-poroelastic medium. The theory, which includes the classic Lord-Shulman (LS) and Green-Lindsay (GL) theories as well as a generalization of the LS model, predicts three inhomogeneous longitudinal waves and one transverse wave, described by potential functions specified by the propagation direction and inhomogeneity angle. The GL model can give a stronger P1-wave thermal attenuation and consequently a stronger velocity dispersion than the LS model. We investigate the influence of inhomogeneity angle, type of incident wave, frequency and surface boundary conditions. The generalized LS model exhibits increased P1-wave thermal attenuation with increasing Maxwell–Vernotte–Cattaneo relaxation time and consequently predicts more interference energy, irrespective if the surface is open or sealed. The inhomogeneity angle affects the energy partitions particularly near the grazing incidence, with a significant interference energy, which must be taken into account to satisfy the energy conservation. The thermal dispersion occurs at frequencies around the thermal relaxation peak, which moves to low frequencies when the conductivity increases.

Scattering from a Buried PEMC Cylinder Illuminated by a Normally Incident Plane Wave Propagating in Free Space

A rigorous solution is presented to the problem of scattering by a perfect electromagnetic conducting (PEMC) circular cylinder buried inside a dielectric half-space that is excited by a normally incident transverse magnetic (TM) plane wave propagating in free space. The plane wave incident on the planar interface separating the two media creates fields transmitting into the dielectric half- space becoming the known primary incident fields for the buried cylinder. When the fields scattered by the cylinder, in response to those fields incident on it, are incident at the interface, they generate fields reflected into the dielectric half-space and fields transmitted into free space. These fields, and the fields scattered by the cylinder are expressed in terms of appropriate cylindrical waves consisting of unknown expansion coefficients which are to be determined. Imposing boundary conditions at the surface of the cylinder and at a point on the planar interface, enables the evaluation of the unknown coefficients. This procedure is then replicated, by considering multiple reflections and transmissions at the planar interface, and multiple scattering by the cylinder, till a preset accuracy is obtained for the reflection coefficient at the particular point on the interface. The refection coefficient at this point is then computed for cylinders of different sizes, to show how it varies with the PEMC admittance of the cylinder, its burial depth, and the permittivity of the dielectric half-space.

Island Rays

This chapter deals with the mathematics of rays that develop around islands. Island rays follow strange trajectories. On the windward side of the island, rays converge slightly, resulting in high waves. Because waves curving around each side of the island converge, waves are lower on the leeward side. Rays that curve around the protected side of the island and spin off into deep water again after turning more than 270 degrees [cross] others on the way. This is an example of how wave refraction around islands can contribute to confused seas. The chapter describes calculations relating to straight and parallel depth contours, focusing on plane wave incident and wave trapping on a ridge, as well as circular depth contours and constant phase lines. It also considers the case of waves and currents moving in exactly opposite directions, asking whether waves can be stopped by opposing streams.

Time-harmonic Analytic Solution for an Acoustic Plane Wave Scattering off an Isotropic Poroelastic Cylinder: Convergence and Form Function

The scattering of a plane wave incident obliquely upon an infinite poroelastic cylinder immersed in inviscid fluid is investigated in this paper. Convergence analysis of the series expansion of the solutions for various interface conditions is conducted and it provides a priori estimates on number of terms necessary for achieving a desired accuracy. In contrast to the existing results in the literature, we consider viscous pore fluid and arbitrary interface discharge efficiency [Formula: see text]. Moreover, the approach presented here does not require any restriction on the viscodynamic operator of the poroelastic equations and hence it can handle general cases beyond the dissipation models proposed by Biot and by Johnson, Koplik and Dashen. The back scattering form function is then calculated from the coefficients of the series solution. Numerical results with various incident angles and interface discharge efficiencies are also presented in this paper.

Electromagnetic diffraction and scattering of a complex-source beam by a semi-infinite circular cone

A complex-source beam (CSB) is used to investigate the electromagnetic scattering and diffraction by the tip of a perfectly conducting semi-infinite circular cone. The boundary value problem is defined by assigning a complex-valued source coordinate in the spherical-multipole expansion of the field due to a Hertzian dipole in the presence of the PEC circular cone. Since the incident CSB field can be interpreted as a localized plane wave illuminating the tip, the classical exact tip scattering problem can be analysed by an eigenfunction expansion without having the convergence problems in case of a full plane wave incident field. The numerical evaluation includes corresponding near- and far-fields.

QUASI-NONUNIQUENESS IN THE SCATTERED FIELD OF A DIELECTRIC CIRCULAR CYLINDER

It is well known that the scattered field of a z polarized plane wave incident on a dielectric circular cylinder can be expanded as an infinite series involving Hankel functions. From numerical calculations of this expansion, Lam and Yedlin [5] observed that the mean square measure, over all space, of the difference of the scattered fields from two or more distinct values of the dielectric constant of the cylinder can take very small values, thereby almost contradicting the uniqueness property. We investigate this phenomenon rigorously using uniform asymptotic expansions of Bessel functions, and from our analysis we determine the spurious values of the dielectric constant which lead to this quasi-nonuniqueness.