Multidomain Chebyshev spectral method for 3-D dc resistivity modeling

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1616-1623 ◽  
Author(s):  
Shengkai Zhao ◽  
Matthew J. Yedlin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Spectral Method ◽  
Direct Current ◽  
Chebyshev Polynomials ◽  
Difference Method ◽  
Dc Resistivity ◽  
Chebyshev Spectral Method ◽  
The Finite Difference Method ◽  
Resistivity Modeling

We use the multidomain Chebyshev spectral method to solve the 3-D forward direct current (dc) resistivity problem. We divided the whole domain into a number of subdomains and approximate the potential function by a separate set of Chebyshev polynomials in each subdomain. At an interface point, we require that both the potential and the flux be continuous. Numerical results show that for the same accuracy the multidomain Chebyshev spectral method is 2 to 260 times faster than the finite‐difference method.

Some refinements on the finite‐difference method for 3-D dc resistivity modeling

Geophysics ◽  
1996 ◽  
Vol 61 (5) ◽  
pp. 1301-1307 ◽  
Author(s):  
Shengkai Zhao ◽  
Matthew J. Yedlin
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Conditions ◽  
Difference Method ◽  
Dirichlet Boundary Conditions ◽  
Percentage Error ◽  
Dc Resistivity ◽  
The Finite Difference Method ◽  
Vertical Contact ◽  
Resistivity Modeling

Two basic refinements of the finite‐difference method for 3-D dc resistivity modeling are presented. The first is a more accurate formula for the source singularity removal. The second is the analytic computation of the source terms that arise from the decomposition of the potential into the primary potential because of the source current and the secondary potential caused by changes in the electrical conductivity. Three examples are presented: a simple two‐layered model, a vertical contact, and a buried sphere. Both accurate and approximate Dirichlet boundary conditions are used to compute the secondary potential. Numerical results show that for all three models, the average percentage error of the apparent resistivity obtained by the modified finite‐difference method with accurate boundary conditions is less than 0.5%. For the vertical contact and the buried sphere models, the error caused by the approximate boundary condition is less than 0.01%.

scholarly journals A Chebyshev Spectral Method for Normal Mode and Parabolic Equation Models in Underwater Acoustics

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Houwang Tu ◽  
Yongxian Wang ◽  
Wei Liu ◽  
Xian Ma ◽  
Wenbin Xiao ◽  
...  
Keyword(s):  
Parabolic Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Spectral Method ◽  
Normal Mode ◽  
Ideal Fluid ◽  
Difference Method ◽  
Acoustic Propagation ◽  
Underwater Acoustic ◽  
Chebyshev Spectral Method

In this paper, the Chebyshev spectral method is used to solve the normal mode and parabolic equation models of underwater acoustic propagation, and the results of the Chebyshev spectral method and the traditional finite difference method are compared for an ideal fluid waveguide with a constant sound velocity and an ideal fluid waveguide with a deep-sea Munk speed profile. The research shows that, compared with the finite difference method, the Chebyshev spectral method has the advantages of a high computational accuracy and short computational time in underwater acoustic propagation.

scholarly journals The Existence of Fourier Coefficients and Periodic Multiplicity Based on Initial Values and One-Dimensional Wave Limits Requirements

2020 ◽  
Vol 10 (2) ◽  
pp. 146
Author(s):  
Adi Jufriansah ◽  
Azmi Khusnani ◽  
Arief Hermanto ◽  
Mohammad Toifur ◽  
Erwin Prasetyo
Keyword(s):  
Finite Difference ◽  
Analytical Solution ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Fourier Analysis ◽  
Spectral Method ◽  
Difference Method ◽  
Hyperbolic Model ◽  
Solution Approach ◽  
The Finite Difference Method

Physical systems in partial differential equations can be interpreted in a visual form using a wave simulation. In particular, the interpretation of the differential equations used is in the nonlinear hyperbolic model, but in its completion, there are some limitations to the stability requirements found. The aim of this study is to investigate the analytical and numerical analysis of a wave equation with a similar unit and fractal intervals using the Fourier coefficient. The method in this research is to use the analytical solution approach, the spectral method, and the finite difference method. The hyperbolic wave equation's analytical solution approach, illustrated in the Fourier analysis, uses a pulse triangle. The spectral method minimizes errors when there is the addition of the same sample grid points or the periodic domain's expansion with a trigonometric basis. Meanwhile, different ways offer a more efficient solution. Based on the research results, the information obtained is that the Fourier analysis illustrates the pulse triangle use to solve the solution. These results are also suitable for adding sample points to the same spectra. Fourier analysis requires a relatively long time to solve one pulse triangle graph to need another solution, namely the finite difference method. However, its use is still limited in terms of stability when faced with more complex problems.

scholarly journals WIDEBAND SATCOM MODEL: EVALUATION OF NUMERICAL ACCURACY AND EFFICIENCY

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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