High-frequency elastodynamic boundary integral inversion using asymptotic phase transformation

Abstract

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[iωp(x)], where p(x) is the field phase, ω 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.