A multi-harmonic finite element method for the micro-Doppler effect, with an application to radar sensing

A finite element method in the spectral domain is proposed for solving wave scattering problems with moving boundaries or, more generally, deforming domains. First, the original problem is rewritten as an equivalent weak formulation set in a fixed domain. Next, this formulation is approximated as a simpler weak form based on asymptotic expansions when the amplitude of the movements or the deformations is small. Fourier series expansions of some geometrical quantities under the assumption that the movement is periodic, and of the solution are next introduced to obtain a coupled multi-harmonic frequency domain formulation. Standard finite element methods can then be applied to solve the resulting problem and a block diagonal preconditioner is proposed to accelerate the Krylov subspace solution of the linear system for high frequency problems. The efficiency of the resulting method is demonstrated on a radar sensing application for the automotive industry