Finite-Difference Solution of the Parabolic Equation Under Horizontal Polar Coordinates

Zhang, Rongshu; Lu, Guizhen; Abomakhleb, Gheit

doi:10.1109/lawp.2017.2753220

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…With the bonus of the development of computational electromagnetics, numerical methods can be used to calculate the RCS of the follow-up release experiments, especially for those with more complex shapes than the spherical clouds generated by point-source release. Among methods of computational electromagnetics, the parabolic equation (PE) method [11,12] proposed by Leontovich and Fock in 1940s, is an excellent one. It studies the energy propagation in a cone region along a given axis under an approximate wave equation.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic scattering of cylindrical artificial electron cloud by using parabolic equation method

Wang,

Xu,

Zhao

et al. 2024

Phys. Scr.

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The ionizable metal vapor released in the ionosphere can artificially generate space electron clouds. They can scatter radio waves at decameter and meter wavelengths so as to realize over-the-horizon propagation. Based on the parabolic equation (PE) method and using Padé-(1,1) polynomial, the electromagnetic scattering characteristics of cylindrical artificial electron clouds are preliminarily studied in this letter. The bistatic radar scattering cross section (RCS) and the ground received field distribution via artificial electron cloud are calculated for various incidence angles at different radio frequencies and distances. The PE method is used here since its advantages of high precision, fast computing and less computing resource occupation over traditional methods. The study of electromagnetic scattering is valuable to the follow-up release experiments for generating electron cloud. It throws a new light on the practical utilization of over-the-horizon radio communication via scattering channel of artificial electron clouds.

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Section: Introductionmentioning

confidence: 99%

Electromagnetic scattering of cylindrical artificial electron cloud by using parabolic equation method

Wang,

Xu,

Zhao

et al. 2024

Phys. Scr.

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“…However, due to the limitation of propagation angle, the calculation area is bound in a long and narrow rectangular area, so it is difficult to solve the problem of radio wave propagation in a large angle area quickly. For this reason, the cylindrical coordinate parabolic equation (CPE) method was proposed, which broke the limit of propagation angle in azimuth [3, 4]. Although its calculation angle can reach

360^{\circ}

, it is not widely used because of the limitation that the calculation amount increases sharply with the increase of propagation distance [5].…”

Section: Introductionmentioning

confidence: 99%

An efficient cylindrical coordinate subgrid parabolic equation model for predicting the power distribution and coverage of radar signals in a complex multi‐scale marine environment

Deng

Liao

Zhang

et al. 2021

Electronics Letters

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An efficient cylindrical coordinate subgrid parabolic equation model is proposed to predict the power distribution and coverage of radar signals in a complex multi‐scale marine environment. The model adopts different grid systems for the multi‐scale marine environment including flat sea surface, islands, ships and other elements, and realizes the transformation between grids through spatial mesh refinement technology. For the prediction of radio wave propagation in a large area complex environment, the model can balance the calculation efficiency and accuracy, thus effectively reducing the memory requirement and CPU computing time. In addition, combined with digital map and radar equation, the power distribution and coverage of radar signal in complex multi‐scale marine environment are calculated. Numerical results verify the correctness and efficiency of the proposed model.

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“…In polar coordinates, the symmetric problem can be described more concisely. A finite difference method was proposed to solve the parabolic equation in polar coordinates in [10]. Britt et al [11] constructed a high-order compact difference scheme for the Helmholtz equation.…”

Section: Introductionmentioning

confidence: 99%

High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates

Zhu¹,

Zhao²

2019

AJCM

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We present a fourth-order finite difference scheme for the Helmholtz equation in polar coordinates. We employ the finite difference format in the interior of the region and derive a nine-point fourth-order scheme. Specially, ghost points outside the region are applied to obtain the approximation for the Neumann boundary condition. We obtain the matrix form of the linear system and the sparsity of the coefficient matrix is favorable for the computation of the Helmholtz equation. The feasibility and accuracy of the method are validated by two test examples which have exact solutions.

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Finite-Difference Solution of the Parabolic Equation Under Horizontal Polar Coordinates

Cited by 3 publications

References 7 publications

Electromagnetic scattering of cylindrical artificial electron cloud by using parabolic equation method

Electromagnetic scattering of cylindrical artificial electron cloud by using parabolic equation method

An efficient cylindrical coordinate subgrid parabolic equation model for predicting the power distribution and coverage of radar signals in a complex multi‐scale marine environment

High-Order Finite Difference Method for Helmholtz Equation in Polar Coordinates

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