An efficient domain decomposition WLP-FDTD method for super-resolution analyses of TR waves

Abstract

In this paper, an efficient domain decomposition (DD) technique is introduced into the unconditionally stable finite-difference time-domain (FDTD) method based on weighted Laguerre polynomials (WLPs) for solving the far-field super-resolution focusing of time reversal (TR) waves. The WLP-FDTD method is very suitable for this multiscale problem due to the sub-wavelength array with some special microstructures such as mental wires. Furthermore, for illustrating the focusing properties with super-resolution of electromagnetic waves beyond the diffraction limit in the far-field region, the TR signal processing technique can make full use of multipath propagation created by various scatterers in a real indoor environment. It has been pointed out from the simulation results that the TR electromagnetic waves can focus with super-resolution in the far field when some special microstructures such as mental wires are loaded around the elements of the receiving array. In simulating electrically large problems, after the whole computational domain is decomposed into multiple subdomains by the DD scheme, the large sparse matrix equation generated by the two-dimensional (2-D) WLP-FDTD method is transformed into some independent small ones. Thus, the solution of the large system of linear equations can be obtained through solving the small independent subsystems and the computational efficiency of WLP-FDTD is improved to some extent. Moreover, the higher-order perfectly matched layer (PML) can be placed very close to the wall and the simulation area can be further reduced accordingly when analyzing the super-resolution focusing properties of TR waves in a multipath indoor environment. Numerical examples of TR wave propagation are included to validate the accuracy and efficiency of the proposed scheme. And the far-field super-resolution simulation result with the resolution of λ/5 is obtained, well beyond the diffraction limit.