FDwave3D: a MATLAB solver for the 3D anisotropic wave equation using the finite-difference method

The article contains a solution to the problem of wave propagation in a one-dimensional rod from the initial impact. A numerical-analytical method is used to solve the problem. The numerical part of the method is based on the application of the idea of the finite difference method. The analytical part uses the concept of Green’s function to solve the problem in terms of the spatial coordinate in the considered area. The results include graphs of the solution obtained at different points in time.

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Splitting the One-Dimensional Wave Equation. Part I: Solving by Finite-Difference Method and Separation Variables

Baghdad Science Journal ◽

10.21123/bsj.2020.17.2(si).0675 ◽

2020 ◽

Vol 17 (2(SI)) ◽

pp. 0675

Author(s):

Shilan Othman Hussein

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Boundary Data ◽

Zeroth Order ◽

Output Force ◽

Ill Posed ◽

The Finite Difference Method ◽

The One

In this study, an unknown force function dependent on the space in the wave equation is investigated. Numerically wave equation splitting in two parts, part one using the finite-difference method (FDM). Part two using separating variables method. This is the continuation and changing technique for solving inverse problem part in (1,2). Instead, the boundary element method (BEM) in (1,2), the finite-difference method (FDM) has applied. Boundary data are in the role of overdetermination data. The second part of the problem is inverse and ill-posed, since small errors in the extra boundary data cause errors in the force solution. Zeroth order of Tikhonov regularization, and several parameters of regularization are employed to decrease errors for output force solution. It is obvious from figures how error affects the results and zeroth order stables the solution.

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WIDEBAND SATCOM MODEL: EVALUATION OF NUMERICAL ACCURACY AND EFFICIENCY

ISPRS Annals of Photogrammetry Remote Sensing and Spatial Information Sciences ◽

10.5194/isprs-annals-v-3-2020-105-2020 ◽

2020 ◽

Vol V-3-2020 ◽

pp. 105-110

Author(s):

A. J. Knisely ◽

A. J. Terzuoli

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Finite Difference Method ◽

Spectral Method ◽

Difference Method ◽

Signal Propagation ◽

Input Function ◽

Propagation Model ◽

Phase Screen ◽

The Finite Difference Method

Abstract. The spectral method is typically applied as a simple and efficient method to solve the parabolic wave equation in phase screen scintillation models. The critical factors that can greatly affect the spectral method accuracy is the uniformity and smoothness of the input function. This paper observes these effects on the accuracy of the finite difference and the spectral methods applied to a wideband SATCOM signal propagation model simulated in the ultra-high frequency (UHF) band. The finite difference method uses local pointwise approximations to calculate a derivative. The spectral method uses global trigonometric interpolants that achieve remarkable accuracy for continuously differentiable functions. The differences in accuracy are presented for a Gaussian lens and Kolmogorov phase screen. The results demonstrate loss of accuracy in each method when a phase screen is applied, despite the spectral method's computational efficiency over the finite difference method. These results provide meaningful insights when discretizing an interior domain and solving the parabolic wave equation to obtain amplitude and phase of a signal perturbation.

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ACCURACY OF FINITE‐DIFFERENCE MODELING OF THE ACOUSTIC WAVE EQUATION

Geophysics ◽

10.1190/1.1440470 ◽

1974 ◽

Vol 39 (6) ◽

pp. 834-842 ◽

Cited By ~ 423

Author(s):

R. M. Alford ◽

K. R. Kelly ◽

D. M. Boore

Keyword(s):

Wave Equation ◽

Finite Difference ◽

Finite Difference Method ◽

Difference Method ◽

Order Accuracy ◽

Order Scheme ◽

The Finite Difference Method ◽

Half Power ◽

Grid Dispersion ◽

Grid Interval

Recent interest in finite‐difference modeling of the wave equation has raised questions regarding the degree of match between finite‐difference solutions and solutions obtained by the more classical analytical approaches. This problem is studied by means of a comparison of seismograms computed for receivers located in the vicinity of a 90-degree wedge embedded in an infinite two‐dimensional acoustic medium. The calculations were carried out both by the finite‐difference method and by a more conventional eigenfunction expansion technique. The results indicate the solutions are in good agreement provided that the grid interval for the finite‐difference method is sufficiently small. If the grid is too coarse, the signals computed by the finite‐difference method become strongly dispersed, and agreement between the two methods rapidly deteriorates. This effect, known as “grid dispersion,” must be taken into account in order to avoid erroneous interpretation of seismograms obtained by finite‐difference techniques. Both second‐order accuracy and fourth‐order accuracy finite‐difference algorithms are considered. For the second‐order scheme, a good rule of thumb is that the ratio of the upper half‐power wavelength of the source to the grid interval should be of the order of ten or more. For the fourth‐order scheme, it is found that the grid can be twice as coarse (five or more grid points per upper half‐power wavelength) and good results are still obtained. Analytical predictions of the effect of grid dispersion are presented; these seem to be in agreement with the experimental results.

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