# A Novel Hybrid Approach for Computing Electromagnetic Scattering from Objects with Honeycomb Structures

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## Abstract

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## 1. Introduction

## 2. Formulation

- In the RSBC, although the volume of the thin unit cell’s wall is removed, we still need to mesh the zero-thickness resistive sheet with the mesh density proportional to the wavenumber in the high-contrast thin-wall materials. However, in the homogenization approach, we only need to mesh the homogenous media with the mesh density proportional to the wavenumber in the media after homogenization. The mesh density of the latter is larger than that of the former, significantly reducing the total number of FEM unknowns. Consequently, the proposed approach yields a better efficiency than the conventional RSBC approach.
- State-of-the-art homogenization theories ignore the edge effect of these unit cells at the boundary of the honeycomb. Such an assumption causes a larger error when the incident angle of the unit cell’s axis of honeycomb structures is large, which is important in practical engineering. Additionally, when the honeycomb boundary is irregularly shaped, the volume fraction of the space occupied by the wall in each honeycomb unit cell is nonuniform, and it is hard to evaluate it accurately. Therefore, the flexibility of the homogenization approach is not as good as that of the RSBC approach. Hence, by using the RSBC on the boundary region, the proposed hybrid approach is more flexible and accurate than the homogenization approach.

## 3. Numerical Results

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Illustration of a honeycomb structure modeled using the proposed hybrid modeling approach.

**Figure 3.**Illustration of different models: (

**a**) inhomogeneous unit cell for FE-BI; (

**b**) homogenous frame for MoM.

**Figure 4.**The monostatic RCS of a panel with size of $62\text{}\mathrm{m}\mathrm{m}\times 54\text{}\mathrm{m}\mathrm{m}\times 10\text{}\mathrm{m}\mathrm{m}$.

**Figure 12.**The computed VV-polarized bistatic RCSs of the wing-like object at 4.5 GHz using different approaches.

**Figure 13.**Geometry of a UVA model with radar-absorbing honeycomb structures: (

**a**) overview of the UVA object; (

**b**) side view of the wing with honeycomb structure.

**Figure 14.**The computed VV polarization. Bistatic RCSs at 6 GHz with and without radar-absorbing honeycomb structures.

Target | RSBC Approach | Hybrid Approach |
---|---|---|

Unknows (FE/BI) | 33045435/2187069 | 22176387/2180004 |

Peak memory (GB) | 341.5 | 265.2 |

Iteration time | 14 h | 9.3 h |

Total time | 17.6 h | 12.5 h |

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**MDPI and ACS Style**

Yuan, X.; Yang, Z.; He, W.; Yang, M.; Sheng, X.
A Novel Hybrid Approach for Computing Electromagnetic Scattering from Objects with Honeycomb Structures. *Electronics* **2023**, *12*, 1851.
https://doi.org/10.3390/electronics12081851

**AMA Style**

Yuan X, Yang Z, He W, Yang M, Sheng X.
A Novel Hybrid Approach for Computing Electromagnetic Scattering from Objects with Honeycomb Structures. *Electronics*. 2023; 12(8):1851.
https://doi.org/10.3390/electronics12081851

**Chicago/Turabian Style**

Yuan, Xiaowei, Zeng Yang, Weijia He, Minglin Yang, and Xinqiing Sheng.
2023. "A Novel Hybrid Approach for Computing Electromagnetic Scattering from Objects with Honeycomb Structures" *Electronics* 12, no. 8: 1851.
https://doi.org/10.3390/electronics12081851