Related papers: Multi-scale methods for wave propagation in hetero…
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…
In this paper we give a survey on various multiscale methods for the numerical solution of second order hyperbolic equations in highly heterogeneous media. We concentrate on the wave equation and distinguish between two classes of…
This paper concerns the analysis of a multiscale method for wave propagation problems in microscopically nonhomogeneous media. A direct numerical approximation of such problems is prohibitively expensive as it requires resolving the…
In geophysics, wave propagation in elastic media is a crucial subject. In this context, seismology has made significant progress as a result of numerous advances, among these stands out the advancement of numerical methods such as the…
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…
Simulating scalar wave propagation in strongly heterogeneous media comes at a steep computational cost, and the widely used approach to simplification - split-step operators - sacrifices accuracy. The recently proposed multi-layer Born…
For over 70 years it has been assumed that scalar wave propagation in (ensemble-averaged) random particulate materials can be characterised by a single effective wavenumber. Here, however, we show that there exist many effective…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
A parabolic equation for the propagation of periodic internal waves over varying bottom topography is derived using the multiple-scale perturbation method. Some computational aspects of the numerical implementation are discussed. The…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
Wave propagation in one-dimensional heterogeneous bistable media is studied using the Schl\"ogl model as a representative example. Starting from the analytically known traveling wave solution for the homogeneous medium, infinitely extended,…
This article considers the computational (acoustic) wave propagation in strongly heterogeneous structures beyond the assumption of periodicity. A high contrast between the constituents of microstructured multiphase materials can lead to…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
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…
This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…
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…