Ronald A. Roberts
Ctr. for Non-Destructive Evaluation ASCII, Iowa State Univ., Ames, IA 50011
A technique for numerical computation of acoustic beam propagation is presented based on a nonasymptotic ray theory. Similar to conventional ray theory, an ansatz of the form (phi)(x)=A(x)e[sup if(x)] is used to transform the Helmholtz equation for time harmonic waves. Imposing A(x) and f(x) are both real leads to two coupled nonlinear PDEs for A(x) and f(x). Conventional ray methods employ an expansion in frequency to decouple one of these equations (eikonal equation) which is solved by ray tracing (method of characteristics). Solution of the remaining transport equation then follows. In the present method, the two coupled nonlinear PDEs are solved self-consistently without an expansion in frequency, resulting in a ray tracing procedure which automatically diffracts at caustics, etc., producing exact field results. Discussion will focus on procedures to insure numerical stability. Application to beam diffraction problems (focusing, beam spreading) will be demonstrated.