Modelling of Disturbance Propagation in Anisotropic Media Using Differential Game Methods
| Authors: | Botkin Nikolay, Research center caesar, Bonn, Germany
Melikyan Arik A., Institute for problems in mechanics, Moscow, Russian Federation
Turova Varvara L., Research center caesar, Bonn, Germany |
|---|
| Topic: | 1.1 Modelling, Identification & Signal Processing |
|---|
| Session: | Applications of Nonlinear Modeling Methods |
|---|
| Keywords: | Waves, Time-optimal control, Optimal trajectories, Differential games, Computer simulations |
|---|
Abstract
The paper is devoted to the modelling of the propagation of acoustic waves at high frequency in anisotropic media. In this case, the WKB approximation results in eikonal equations whose Hamiltonians are neither convex nor concave in the impulse variable so that the Fermat principle fails. In this paper, methods of differential games are adopted for the analysis of wave propagation. If the Hamiltonian of a differential game approximates the Hamiltonian of the eikonal equation, then the solution to the game approximates the phase function satisfying the eikonal equation. Classification of singularities in differential games associated with wave propagation problems is done. Numerical results are presented for wave velocity surfaces typical for anisotropic quartz crystals.
