Coupling of finite elements and hierarchical boundary elements for dynamic soil-structure interaction problems

Abstract

This paper discusses the coupling of finite element and fast boundary element methods based on hierarchical matrices to solve problems of visco-elastodynamic wave propagation involving dynamic soil-structure interaction in the frequency domain. Three coupling methodologies are presented and their computational performance is assessed through numerical examples. It is demonstrated that a direct coupling approach, in which the boundary element domain is condensed into an equivalent dynamic stiffness matrix, is the least efficient. Iterative procedures provide a valuable alternative; the efficiency of these algorithms strongly depends on the kind of boundary conditions applied to each subdomain, however. The fastest convergence is observed if Neumann boundary conditions are imposed on the most stiff subdomain. Aitken's Δ2-method is employed in these schemes for the calculation of an optimized interface relaxation parameter in order to ensure and speed up the convergence. A monolithic coupling approach is presented as well, providing a simultaneous solution of the governing equations while avoiding the assembly of a dynamic soil stiffness matrix.