A Fast Solver for the Elastic Scattering of Multiple Particles

Abstract

Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert the boundary value problem of the elastic wave equation into a coupled boundary value problem of Helmholtz equations. Based on single, double, and combined layer potentials with the simpler Green's function of the Helmholtz equation, we present three different boundary integral equations for the coupled boundary value problem. The well-posedness of the new integral equations are established. Computationally, a scattering matrix based method is proposed to evaluate the elastic wave for arbitrarily shaped particles. The method uses the local expansion for the incident wave and the multipole expansion for the scattered wave. The linear system of algebraic equations is solved by GMRES with fast multipole method (FMM) acceleration. Numerical results show that the method is fast and highly accurate for solving the elastic scattering problem with multiple particles.

References in corpus (5)

• Quadrature by Expansion: A New Method for the Evaluation of Layer Potentials
• A fast and robust solver for the scattering from a layered periodic structure containing multi-particle inclusions
• An accurate boundary element method for the exterior elastic scattering problem in two dimensions
• A fast solver for multi-particle scattering in a layered medium
• An FFT-accelerated direct solver for electromagnetic scattering from penetrable axisymmetric objects

Cited by in corpus (5)

• An inverse acoustic-elastic interaction problem with phased or phaseless far-field data
• Fast inverse elastic scattering of multiple particles in three dimensions
• Inverse obstacle scattering for elastic waves in the time domain
• An Efficient Finite Difference-Based PML Technique for Acoustic Scattering Problems
• A highly accurate boundary integral method for the elastic obstacle scattering problem