A fast solver for elastic scattering from axisymmetric objects by boundary integral equations

TL;DR

This paper introduces a fast, high-order boundary integral solver for 3D elastic scattering from axisymmetric objects, combining Helmholtz decomposition, FFT acceleration, and regularization techniques for efficiency and accuracy.

Contribution

It develops a novel boundary integral formulation using Helmholtz decomposition and an FFT-accelerated solver for elastic scattering from axisymmetric bodies, enhancing computational speed and precision.

Findings

Efficiently solves elastic scattering problems with high accuracy.

Handles geometries with corners at various wave numbers.

Demonstrates significant speedup over traditional methods.

Abstract

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.