Seismic Wave Scattering Through a Compressed Hybrid BEM/FEM Method

TL;DR

This paper reviews a hybrid BEM/FEM method for efficiently approximating seismic wave scattering in semi-infinite domains, balancing accuracy and computational resources for engineering applications.

Contribution

It introduces a banded matrix approximation of BEM matrices integrated with FEM to reduce memory use while maintaining acceptable accuracy.

Findings

The method achieves lower memory requirements compared to classical BEM.

Benchmark tests show good accuracy in time and frequency domains.

The approach is suitable for practical engineering decision-making.

Abstract

Approximated numerical techniques, for the solution of the elastic wave scattering problem over semi-infinite domains are reviewed. The approximations involve the representation of the half-space by a boundary condition described in terms of 2D boundary element discretizations. The classical BEM matrices are initially re-written into the form of a dense dynamic stiffness matrix and later approximated to a banded matrix. The resulting final banded matrix is then used like a standard finite element to solve the wave scattering problem at lower memory requirements. The accuracy of the reviewed methods is benchmarked against the classical problems of a semi-circular and a rectangular canyon. Results are presented in the time and frequency domain, as well as in terms of relative errors in the considered approximations. The main goal of the paper is to give the analyst a method that can be used at the practising level where an approximate solution is enough in order to support engineering decisions.