Abstract
A proper dielectric coating can reduce the electromagnetic scattering of the conducting object significantly so that it cannot be detected by the radar. However, when the object contains a thin coating, fine grid size is needed to discretize the thin coating in the conventional finite-difference time-domain (FDTD) algorithm, which increases the amount of memory and computational time significantly. To overcome this dilemma, we present a transformation optics-based FDTD (TO-FDTD) algorithm to accelerate the solution of electromagnetic scattering from objects with thin dielectric coatings. Two kinds of novel TO-FDTD models are proposed in this paper for a coated cylinder and a coated arbitrary polygonal cylinder, respectively. Through coordinate transformation, the size of the object remains unchanged while its thin coating is enlarged to a thicker one, meaning that it can be simulated by the FDTD algorithm with uniform coarse grids instead of fine grids. The transformed material parameters become inhomogeneous and anisotropic in the transformed region, which can be obtained by solving a Jacobian transformation matrix. We then develop a stable FDTD algorithm for solving anisotropic Maxwell’s equations. Bistatic scatterings of coated cylinders and a coated polygonal cylinder are solved by the TO-FDTD algorithm proposed in this paper, respectively. The result of the TO-FDTD algorithm matches well with the exact value and the result of the commercial software Comsol. The computational efficiency and accuracy of the proposed TO-FDTD algorithm are validated by numerical experiments. Numerical results show that the TO-FDTD algorithm has higher computational accuracy than the conventional FDTD algorithm that fails to simulate the absorbing property of the coating, when the same coarse grid size is used in the simulation. Under the same level of accuracy, the proposed TO-FDTD method can improve the computational efficiency by 62-63 times than the conventional FDTD method with fine grids in the simulations in the paper.
Highlights
Scattering of dielectric coated objects has attracted significant interest in recent years because of its important applications from a modern military perspective
The electromagnetic scattering of such composite objects can be solved by three typical numerical techniques: the integral equation based moment methods, wave equation based finite element method (FEM), and Maxwell’s differential equations based finite difference time domain (FDTD) method
We propose a novel transformation optics-based finite-difference time-domain (FDTD) (TO-FDTD) algorithm to realize fast solution of scattering from thin dielectric coated objects
Summary
Scattering of dielectric coated objects (e.g. aircrafts or ships) has attracted significant interest in recent years because of its important applications from a modern military perspective. An alternative method to solve the electromagnetic problem of small structures in a large computational domain is the transformation optics (TO) based local mesh refinement method proposed by Liu et al [29] This method can eliminate the late-time instability by using the field transformation, rather than temporal and spatial field interpolations, compared with the subgridding scheme. Electric/magnetic field errors of the coarse-fine interface due to its absence This method is unsuitable to solve the multi-scale problem of thin dielectric coated objects, since the objects and coatings are both enlarged by its transformation. TO-FDTD METHOD For the scattering analysis of a thin dielectric coated perfect electric conducting (PEC) object, we first enlarge the thin coating to a thicker one in the transformed region, while the PEC body remains unchanged, using coordinate transformation. Based on the form invariance of Maxwell’s equations under coordinate transformation, we propose a stable anisotropic FDTD algorithm for resolving electric/magnetic fields in the transformed region. Other solving processes for the coated arbitrary polygonal cylinder are the same as those for the coated cylinder
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