Electromagnetic interrogation and the Doppler shift using the method of mappings

We consider the electromagnetic detection of hidden moving or oscillating conductive targets. The resulting mathematical problem involves computation of a Doppler shift for an electromagnetic wave reflecting from a moving interface. This entails solving Maxwell’s equations on a domain changing in time. We employ the method of mappings to transform the problem to one of computing solutions of a Maxwell system with time dependent coefficients on a fixed reference domain. Thus we obtain a problem that is eminently tractable with finite element or finite difference time domain methods. Accuracy of numerical solutions is illustrated with computations for a number of different velocities for the moving interface. AMS subject classifications: 35Q61,83C50,83C22,65M32.