Discrete Optimization Model for 2-Dimensional Energised Waves
Energised waves, a coinage due to Reju et al (2001) are waves characterised by diffusion effects (Odio, Pain). Such waves are common in acoustics, ocean waves and many other wave propagation phenomena that involve propagation of energy. Reju (1995) was the first to apply the Extended Conjugate Gradient Method (ECGM) to the optimal control of classical wave propagation problem and with a specific extension to energised waves carried out by Waziri (2006). Computational procedures of Reju and Waziri are semi-analytic in nature employing in each case a direct methodology that is finally employed in the implementation of the ECGM. This research therefore aims at employing a discretization procedure to the search of optimal solutions of the 2-dimensional energised wave propagation problem and so contributing to the unified theory of the ECGM solvable problems. Moreover, the research seeks to study the improvement (or otherwise) of the discrete model over the semi-analytic approach with its associated iterative properties.
The Research project will be divided into two parts, namely, the discretization of the Hamiltonian component and then followed by the discrete ECGM operator construction.