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Simultaneous Differential Equations
Published in L.M.B.C. Campos, Simultaneous Systems of Differential Equations and Multi-Dimensional Vibrations, 2019
The conservation law (7.433a, b) valid in the ray approximation can be explained as follows: (i) the high-frequency waves are like sound rays with wavelength small compared with the lengthscale of variations of cross-section; (ii) thus, the wave reflection from the walls is negligible, and the acoustic horn acts as a ray tube along which the acoustic energy per unit length is conserved. The opposite limit to (note 7.25) the ray or high-frequency approximation (7.431d) = (7.435a) is the low-frequency or compactness limit of scattering (7.435c) when the wavelength is much larger than the lengthscale, for example, wave reflection and transmission (notes 7.44–7.52) at an abrupt change of cross-section: waves:2kL2>>1:rays,kL∼1refraction/diffraction,kL<<1scattering
Propagation II:Mathematical Models (Part One)
Published in Paul C. Etter, Underwater Acoustic Modeling and Simulation, 2017
Doran and Fredricks (2007) used the level-set method, which is a fixed-grid method for generating solutions to the high-frequency approximation to the wave equation. In this method, the user controls the underlying grid and thus the accuracy of the solution. Osher and Sethian (1988) developed generic computational techniques that are referred to as PSC (propagation of surfaces under curvature) algorithms.
Asymptotic analysis of wave scattering on a periodic boundary
Published in C Constanda, J Saranen, S Seikkala, Integral methods in science and engineering, 2020
In [3] and [4] the authors have developed a new asymptotic theory of scattering by an echelette grating and smooth periodic (sinusoidal) boundary in the high frequency approximation based on GTD and the method of summation of MDF. These were the first examples of GTD applied to scattering by diffraction gratings.
Unconditionally stable FDTD-based approach for scattering from an object above random rough surface
Published in Waves in Random and Complex Media, 2022
Shuo Liu, Bin Zou, Lamei Zhang
There are also limitations to the approach presented here. Being a numerical method, although the proposed approach can be applied to any frequency in theory, it consumes a lot of computing resources and time when the frequency is high. Constrained by the computing power and available resources of the current computer, it can only calculate the case of C-band and below. Beyond this frequency, it may resort to high-frequency approximation methods. Additionally, due to the truncation effect of the infinite rough surface, there are always some ‘inaccurate’ regions with large scattering angles in the upper half-space. Finally, it is worth mentioning that when the roughness of the rough surface is very small, inaccuracies will occur when using FDTD and its varieties due to the FDTD lattice’s stair-stepped approximation.