Numerical solution of the parabolic equation representing eletromagnetic wave propagation in the troposphere using box method

AbstractThis work provides an introduction to one of the most widely used advanced methods for wave propagation modeling, the Parabolic Equation (PE) method, with emphasis on its application to tropospheric radio propagation in coastal and maritime regions. The assumptions of the derivation, the advantages and drawbacks of the PE, the numerical methods for solving it, and the boundary and initial conditions for its application to the tropospheric propagation problem are briefly discussed. More details are given for the split-step Fourier-transform (SSF) solution of the PE. The environmental input to the PE, the methods for tropospheric refractivity profiling, their accuracy, limitations, and the average refractivity modeling are also summarized. The reported results illustrate the application of finite element (FE) based and SSF-based solutions of the PE for one of the most difficult to treat propagation mechanisms, yet of great significance for the performance of radars and communications links working in coastal and maritime zones — the tropospheric ducting mechanism. Recent achievements, some unresolved issues and ongoing developments related to further improvements of the PE method application to the propagation channel modeling in sea environment are highlighted.

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Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽

10.1190/1.1440881 ◽

1978 ◽

Vol 43 (6) ◽

pp. 1099-1110 ◽

Cited By ~ 169

Author(s):

Albert C. Reynolds

Keyword(s):

Wave Propagation ◽

Reflection Coefficient ◽

Finite Difference ◽

Boundary Conditions ◽

Numerical Solution ◽

Neumann Boundary ◽

Synthetic Seismograms ◽

Neumann Boundary Conditions ◽

Numerical Calculations ◽

Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

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Numerical Solution of a Kind of Fractional Parabolic Equations via Two Difference Schemes

Abstract and Applied Analysis ◽

10.1155/2013/828764 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 21

Author(s):

Abdon Atangana ◽

Dumitru Baleanu

Keyword(s):

Parabolic Equation ◽

Fractional Calculus ◽

Numerical Solution ◽

Parabolic Equations ◽

Difference Schemes ◽

Stability And Convergence ◽

Implicit Schemes ◽

The Stability

A kind of parabolic equation was extended to the concept of fractional calculus. The resulting equation is, however, difficult to handle analytically. Therefore, we presented the numerical solution via the explicit and the implicit schemes. We presented together the stability and convergence of this time-fractional parabolic equation with two difference schemes. The explicit and the implicit schemes in this case are stable under some conditions.

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