Composite electromagnetic scattering from a ship located on one-dimensional sea surface with time-domain hybrid method

With the development of broadband radar technology, transient composite scattering from a target and a randomly rough surface has aroused a great interest in oceanic remote sensing, target identification, and military applications. Time-domain integral equation (TDIE) is an effective numerical method of analyzing transient and broadband electromagnetic problems. However, the high computational complexity of numerical methods restricts its applications in analyzing the electrically large rough surfaces. To improve computational efficiency, hybrid methods have been developed by combining an analytical method with a numerical algorithm, and used to solve the electromagnetic scattering of a composite model. In these hybrid methods, numerical methods are used to calculate the scattering from a target, and analytical methods are employed to solve the scattering from a rough surface. To our knowledge, most of the hybrid methods for composite electromagnetic scattering are frequency-domain algorithms and used to investigate composite scattering from a rough surface with a target above it. Few papers have been published on the analysis of transient scattering from a rough surface with a target by using the time-domain hybrid methods. In the present paper, an efficient time-domain hybrid method that combines time-domain Kirchhoff approximation (TDKA) with TDIE is first designed to investigate the transient electromagnetic scattering from a ship located on a randomly rough sea surface. In this hybrid method, the ship and its adjacent sea surface are chosen as TDIE region and the rest of the rough surface is TDKA region. Considering the interactions between the TDIE region and the TDKA region, the hybrid TDIE-TDKA formula is derived and solved with an iterated marching-on-in-time method. Initially, the induced currents of the TDIE region are acquired by solving TDIE. Then, the currents in the TDKA region are obtained via TDKA method. The interactions between the currents in the TDKA region are neglected. The efficiency and accuracy of the hybrid TDIE-TDKA method depend on the size of the TDIE region. The minimum length of sea surface in the TDIE region is at least the size of the ship due to the strong interactions between the ship and its adjacent sea surface. Numerical results show that the hybrid TDIE-TDKA method presented in this paper is accurate and efficient compared with the full TDIE. Moreover, the influences of the ship size, the wind speed, the incident angle, and the depth of the ship immersing in sea surface on the backscattered far magnetic field are discussed in detail.