Related papers: Propagation of one and two-dimensional discrete wa…
We study the propagation properties of the solutions of the finite-difference space semi-discrete wave equation on an uniform grid of the whole Euclidean space. We provide a construction of high frequency wave packets that propagate along…
We study the propagation, observation and control properties of the 1-d wave equation on a bounded interval discretized in space using the quadratic classical finite element approximation. A careful Fourier analysis of the discrete wave…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
This study explores the use of fractional calculus as a possible tool to model wave propagation in complex, heterogeneous media. We illustrate the methodology by focusing on elastic wave propagation in a one-dimensional periodic rod. The…
This work is concerned with the construction of Gaussian Beam (GB) solutions for the numerical approximation of wave equations, semi-discretized in space by finite difference schemes. GB are high-frequency solutions whose propagation can be…
Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
The analysis of wave propagation problems in linear damped media must take into account both propagation features and attenuation process. To perform accurate numerical investigations by the finite differences or finite element method, one…
In this paper we study the dispersive properties related to a model of peridynamic evolution, governed by a non local initial value problem, in the cases of two and three spatial dimensions. The features of the wave propagation…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
We study two-dimensional wave propagation in materials whose properties vary periodically in one direction only. High order homogenization is carried out to derive a dispersive effective medium approximation. One-dimensional materials with…
We study the coherent propagation and incoherent diffusion of in-plane elastic waves in a two dimensional continuum populated by many, randomly placed and oriented, edge dislocations. Because of the Peierls-Nabarro force the dislocations…
The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
In this paper, we discuss the transport phenomena of electromagnetic waves in a two-dimensional random system which is composed of arrays of electrical dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc. Am. B…
The aim of this article is to study the attenuation of transient low-frequency waves in 2D lattices in both plane and antiplane problems. The main idea of this article is that analytical solutions to problems of mechanics of discrete…
We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations…
Numerical solutions to hyperbolic partial differential equations, involving wave propagations in one direction, are subject to several specific errors, such as numerical dispersion, dissipation or aliasing. In multi-dimensions, where the…
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
We propose wave and ray approaches for modelling mid- and high- frequency structural vibrations through smoothed joints on thin shell cylindrical ridges. The models both emerge from a simplified classical shell theory setting. The ray model…