### ASA 124th Meeting New Orleans 1992 October

## 4pPA7. High-frequency elastodynamic boundary integral inversion using
asymptotic phase transformation.

**Ronald A. Roberts
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*Ctr. for Non-Destructive Eval. ASCII, Iowa State Univ., Ames, IA 50011
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Use of conventional finite element or boundary element computational
methods for problems of time-harmonic elastic wave transmission, diffraction,
and surface wave generation at a nonplanar fluid--solid interface become
inefficient at high frequencies due to the fineness of discretization required
for numerical convergence. A more efficient computational procedure has been
developed that exploits the field phase as predicted by high-frequency
asymptotic analysis (i.e., the geometrical theory of diffraction, or GTD). In
this method, the boundary integral equation which governs elastic wave
transmission is transformed by assuming a solution in the form of the GTD
ansatz A(x)exp[i(omega)p(x)], where p(x) is the field phase, (omega) is time
harmonic frequency, and A(x) is the field amplitude. The phase p(x) is
prescribed analytically through solution of the leading term eikonal equations
of GTD. The transformed boundary integral equation is then solved numerically
for the amplitudes A(x). The amplitudes A(x) will have a narrow spatial
frequency spectral bandwidth, and hence can be efficiently calculated. This
approach exploits the strengths of the GTD eikonal equation solutions while
avoiding the analytical pitfalls encountered in the GTD transport equations.