GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Numerical solution of the Helmholtz equation in 2D and 3D using a high-order Nystro¨m discretization
Journal of Computational Physics
Journal of Computational Physics
Multilevel fast multipole algorithm for elastic wave scattering by large three-dimensional objects
Journal of Computational Physics
A perfectly matched layer for the absorption of electromagnetic waves
Journal of Computational Physics
A system of boundary integral equations for the transmission problem in acoustics
Applied Numerical Mathematics
Journal of Computational Physics
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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(N^4^/^3logN) operations, and it shows algebraic convergence. Several numerical experiments are provided to demonstrate the efficiency of the method.