A Simple and Efficient Regularization Method for 3D BEM: Application to Frequency-Domain Elastodynamics

TL;DR

This paper introduces a simple, efficient regularization technique for 3D boundary element methods, improving accuracy in frequency-domain elastodynamics problems through analytical integral expressions and numerical validation.

Contribution

It presents a novel regularization method leveraging analytical singular integral expressions for 3D BEM, enhancing computational efficiency and accuracy.

Findings

Accurate results for elastodynamic problems in frequency domain

Close agreement with semi-analytical solutions

Effective regularization for boundary element integral equations

Abstract

An efficient and easy-to-implement method is proposed to regularize integral equations in the 3D boundary element method (BEM). The method takes advantage of an assumed three-noded triangle discretization of the boundary surfaces. The method is based on the derivation of analytical expressions of singular integrals. To demonstrate the accuracy of the method, three elastodynamic problems are numerically worked out in the frequency domain: a cavity under harmonic pressure, diffraction of a plane wave by a spherical cavity, and amplification of seismic waves in a semispherical alluvial basin (the second one is also investigated in the time domain). The numerical results are compared to semi-analytical solutions; a close agreement is found for all problems, showing the accuracy of the proposed method.