NEW TIME-EXPLICIT ASYMPTOTIC METHOD FOR THE SOLUTION OF AN EXACT CONTROLLABILITY PROBLEM OF SCATTERING WAVES

In this paper a new time-explicit asymptotic method is presented through introducing an auxiliary parameter for the solution of an exact controllability problem of scattering waves. Based on an exact control function, the asymptotic iteration is controlled by the auxiliary parameter and the optimal auxiliary parameter is updated during the iteration based on the existing or current iterated solutions of the wave equation. The numerical results show that the new method presented has a significant advantage over the purely asymptotic method in the history of convergence and has the ability to solve the scattering by the multi-bodies.