Furtivity and masking problems in time dependent electromagnetic obstacle scattering

Abstract

Summary form only given. We consider furtivity and masking problems in time dependent three dimensional electromagnetic obstacle scattering. That is we propose a criterion based on a merit function to minimize or to mask the electromagnetic field scattered by a bounded obstacle when hit by an incoming electromagnetic field and with respect to this criterion we derive the optimal strategy. These problems are natural generalizations to the context of electromagnetic scattering of the furtivity problem in time dependent acoustic obstacle scattering. We propose mathematical models of the furtivity and masking time dependent three dimensional electromagnetic scattering problems that consist in optimal control problems for the Maxwell equations. These control problems are approached using the Pontryagin maximum principle. We formulate the first order optimality conditions for the control problems considered as exterior problems defined outside the obstacle for systems of partial differential equations. Moreover the first order optimality conditions derived are solved numerically with a highly parallelizable numerical method based on a perturbative series. We assess and validate the mathematical models and the numerical method proposed analyzing the numerical results obtained with a parallel implementation of the numerical method in several experiments on test problems. Really impressive speed up factors are obtained executing the algorithms on a parallel machine when the number of processors used in the computation ranges between 1 and 100. Some virtual reality applications and some animations relative to the numerical experiments can be found in the website: http://www.econ.unian.it/reechioni/w10/. Finally further developments of the ideas presented here will be discussed.