An Inverse Moving Point Source Problem in Electromagnetics

Abstract. This paper is concerned with an inverse moving point source problem in electromagnetics. The aim is to reconstruct the moving orbit from the tangential components of magnetic fields taken at a finite number of observation points. The distance function between each observation point and the moving point source is computed by solving a nonlinear ordinary differential equation with an initial value. This ODE system only involves the measurement data from the tangential trace of the magnetic field at observation points. As a consequence, the dynamical measurement data recorded at four noncoplanar points are sufficient to reconstruct the orbit function. A Lipschitz stability is established for the inverse problem, and numerical experiments are reported to demonstrate the effectiveness of the proposed method. Our numerical examples show that the reconstruction error is proportional to the noise level and that the wave speed significantly impacts the results.