A Numerical Solution of the Helmholtz Problem via Controllability Technique Manel Layouni Amamou Faculty of Science Mathematics Physics and Natural of Tunis, University Tunis-El Manar, Tunisia, [email protected] Abstract In this paper, we present a numerical solution of the Helmholtz scattering problem based on controllability Technique [1]. First, we show that solving the Helmholtz problem returns to minimizing a cost function 1 J(ψ, ψt ) ≡ 2 Z (| 5 (ψ(x, T ) − ψ(x, 0))|2 + |ψt (x, T ) − ψt (x, 0)|2 )dx Υ subject to the wave equation. Then, we implement a Conjugate Gradient Method to solve the optimal control problem. Finally, and in order to prove our algorithm, we perform some numerical simulations with several physical parameters of the scattering problem. Keywords: Helmholtz equation, optimal control problem, conjugate gradient method. References [1] R. Glowinski, J. Periaux and J. Toivanen, Time-Periodic Solutions of Wave Equation via Controllability and Fictitious Domain Methods, Sixth International Conference on Mathematical and Numerical Aspects of Wave Propagation, 2003.