  Fast and high-order accurate algorithms for three dimensional elastic
scattering are of great importance when modeling physical phenomena in
mechanics, seismic imaging, and many other fields of applied science. In this
paper, we develop a novel boundary integral formulation for the three
dimensional elastic scattering based on the Helmholtz decomposition of elastic
fields, which converts the Navier equation to a coupled system consisted of
Helmholtz and Maxwell equations. An FFT-accelerated separation of variables
solver is proposed to efficiently invert boundary integral formulations of the
coupled system for elastic scattering from axisymmetric rigid bodies. In
particular, by combining the regularization properties of the singular boundary
integral operators and the FFT-based fast evaluation of modal Green's
functions, our numerical solver can rapidly solve the resulting integral
equations with a high-order accuracy. Several numerical examples are provided
to demonstrate the efficiency and accuracy of the proposed algorithm, including
geometries with corners at different wave number.
