A fast high-order algorithm for the multiple cavity scattering

ABSTRACT

A fast high-order algorithm is proposed for solving the electromagnetic scattering from multiple cavities embedded in an infinite ground plane. By means of a transparent boundary condition, we transform the multiple cavity scattering problem into the Helmholtz equations restricted to each cavity with coupled nonlocal boundary conditions on the apertures. Then a fourth-order method in each cavity is constructed. It results in a big system involving the Helmholtz equations with the coupled transparent boundary conditions, which is further reduced to a small system that includes only the coupling of the aperture system of each cavity. The cost of calculating the radar cross section is $\mathcal{O}\left(NMlog\right(nM\left)\right)$ with $N\times M$ meshes in each cavity, where n is the number of separate cavities. Numerical experiments with large wave numbers are presented to verify the efficiency of the proposed method.

Keywords:

• Multiple cavity scattering
• compact high-order method
• Helmholtz equation
• transparent boundary condition
• large wave number

2010 AMS Subject Classification:

• 65N06
• 65N22

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China (grant no. 11401208) and Natural Science Foundation of Hebei Province (grant no. A2016502001).