Application of hierarchical matrices to boundary element methods for elastodynamics based on Greenʹs functions for a horizontally layered halfspace

This paper presents the application of hierarchical matrices to boundary element methods for elastodynamics based on Greenʹs functions for a horizontally layered halfspace. These Greenʹs functions are computed by means of the direct stiffness method; their application avoids meshing of the free surface and the layer interfaces. The effectiveness of the methodology is demonstrated through numerical examples, indicating that a significant reduction of memory and CPU time can be achieved with respect to the classical boundary element method. This allows increasing the problem size by one order of magnitude. The proposed methodology therefore offers perspectives to study large scale problems involving three-dimensional elastodynamic wave propagation in a layered halfspace, with possible applications in seismology and dynamic soil–structure interaction.