A fast and high-order method for the three-dimensional elastic wave scattering problem

In this paper we present a fast and high-order boundary integral equation method for the elastic scattering by three-dimensional large penetrable obstacles. The algorithm extends the method introduced in [5] for the acoustic surface scattering to the fully elastic case. In our algorithm, high-order accuracy is achieved through the use of the partition of unity and a semi-classical treatment of relevant singular integrals. The computational efficiency associated with the nonsingular integrals is attained by the method of equivalent source representations on a Cartesian grid and Fast Fourier Transform (FFT). The resulting algorithm computes one matrix–vector product associated with the discretization of the integral equation with O(N4/3logN) operations, and it shows algebraic convergence. Several numerical experiments are provided to demonstrate the efficiency of the method.