Coupled finite element - hierarchical boundary element methods for dynamic soil-structure interaction in the frequency domain

Abstract

SUMMARY This paper discusses the coupling of finite element and fast boundary element methods for the solution of dynamic soil–structure interaction problems in the frequency domain. The application of hierarchical matrices in the boundary element formulation allows considering much larger problems compared to classical methods. Three coupling methodologies are presented and their computational performance is assessed through numerical examples. It is demonstrated that the use of hierarchical matrices renders a direct coupling approach the least efficient, as it requires the assembly of a dynamic soil stiffness matrix. Iterative solution procedures are presented as well, and it is shown that the application of such schemes to dynamic soil–structure interaction problems in the frequency domain is not trivial, as convergence can hardly be achieved if no relaxation procedure is incorporated. Aitken's Δ2-method is therefore employed in sequential iterative schemes for the calculation of an optimized interface relaxation parameter, while a novel relaxation technique is proposed for parallel iterative algorithms. It is demonstrated that the efficiency of these algorithms strongly depends on the boundary conditions applied to each subdomain; the fastest convergence is observed if Neumann boundary conditions are imposed on the stiffest subdomain. The use of a dedicated solver for each subdomain hence results in a reduced computational effort. A monolithic coupling strategy, often used for the solution of fluid–structure interaction problems, is also introduced. The governing equations are simultaneously solved in this approach, while the assembly of a dynamic soil stiffness matrix is avoided. Copyright © 2013 John Wiley & Sons, Ltd.