Simulation of Acoustic Wave Propagation in Anisotropic Media Using Dynamic Programming Technique

Abstract

It is known that the Hamiltonian of the eikonal equation for an anisotropic medium may be nonconvex, which excludes the application of Fermat's minimum-time principle related to minimum-time control problems. The idea proposed in this paper consists in finding a conflict control problem (differential game) whose Hamiltonian coincides with the Hamiltonian of the eikonal equation. It turns out that this is always possible due to Krasovskii's unification technique. Having such a differential game allows us to apply dynamic programming methods to computing the value function of the game, and therefore to describe the propagation of wave fronts. This method is very appropriate for the simulation of wave patterns in surface acoustic wave biosensors. Numerical computations given in this paper prove the feasibility of the approach proposed.