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In this paper, the Adaptive Modified Characteristic Basis Function Method (AMCBFM) is proposed for quickly simulating electromagnetic scattering from a one-dimensional perfectly electric conductor (PEC) rough surface. Similar to the traditional characteristic basis function method (CBFM), Foldy-Lax multiple scattering equations are applied in order to construct the characteristic basis functions (CBFs). However, the CBFs of the AMCBFM are different from those of the CBFM. In the AMCBFM, the coefficients of the CBFs are first defined. Then, the coefficients and the CBFs are used to structure the total current, which is used to represent the induced current along the rough surface. Moreover, a current criterion is defined to adaptively halt the order of the CBFs. The validity and efficiency of the AMCBFM are assessed by comparing the numerical results of the AMCBFM with the method of moments (MoM). The AMCBFM can effectively reduce the size of the matrix, and it costs less than half the CPU time used by the MoM. Moreover, by comparing it with the traditional CBFM, the AMCBFM can guarantee the accuracy, reduce the number of iterations, and achieve better convergence performance than the CBFM does. The second order of the CBFs is set in the CBFM. Additionally, the first order of the CBFs of the AMCBFM alone is sufficient for this result.

Electromagnetic (EM) scattering from rough surface has been widely studied and applied in the research areas of marine communication, target detection, and stealth technology [

In this paper, the Adaptive Modified Characteristic Basis Function Method (AMCBFM) [

The remainder of this paper is organized as follows. In Section

Assume that there is a tapered plane wave

Geometric model of the EM scattering from a PEC rough surface.

For a Horizontal (H) polarized incident wave, the surface integral equation for this scattering problem is [

For the Vertical (V) case, the surface integral equation is as follows [

Analyzing (

In the AMCBFM, the

Assuming the total current

Taking (

The first total current

Taking (

The

The validity and efficiency of the AMCBFM are first assessed by comparing its results with the results that were obtained from the CBFM and the MoM. Both the H and V polarized incident waves are considered. In Figure

The bistatic scattering coefficients obtained by the different methods. (a) H polarization and (b) V polarization.

The currents obtained by the AMCBFM and the CBFM. (a) H polarization and (b) V polarization.

Moreover, in Table

The CPU time and the percentage error of the AMCBFM and the CBFM.

polarization | method | CPU Time (seconds) | Percentage error |
---|---|---|---|

H | AMCBFM | 6.132 | |

CBFM | 6.689 | | |

MoM | 14.016 | —— | |

| |||

V | AMCBFM | 6.243 | |

CBFM | 6.647 | | |

MoM | 14.138 | —— |

One may note that only one sample of the rough surface is used in Figures

The results of the AMCBFM with different error thresholds.

polarization | Error threshold | Orders of SCBFs | Percentage error | CPU Time (seconds) |
---|---|---|---|---|

H | | 1 | | 6.022 |

| 1 | | 6.068 | |

| 1 | | 6.131 | |

| 2 | | 9.625 | |

| 6 | | 43.368 | |

| ||||

V | | 1 | | 6.164 |

| 1 | | 6.287 | |

| 1 | | 6.302 | |

| 2 | | 9.188 | |

| 2 | | 9.172 |

In this paper, the AMCBFM was used to simulate the EM scattering from a Gaussian rough surface. Good agreement between the AMCBFM and the MoM was found. In addition, the AMCBFM costs less than half the CPU time of the MoM. Furthermore, compared with the traditional CBFM, the lower order of the CBFs of the AMCBFM is sufficient for guaranteeing the accuracy. Note that the scattering model is only a 2D model. In the future, this method will be expanded to solve the more realistic 3D scattering problem. In addition, this method can also be applied to calculate the dielectric rough surface with a cylinder located above it. Finally, the AMCBFM can be combined with the compressing sensing technology in order to solve the EM scattering over a frequency band.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 61501004 and 61722101), the Natural Science Foundation of Anhui Province (Grant Nos. 1608085QF141 and 1608085MF135), and the Provincial Program of Natural Science of Anhui Higher Education (Grant No. KJ2015A073).