This chapter reviews recent developments in the strategies for the fast
solution of boundary element systems of equations for large scale 3D elastic
problems. Both isotropic and anisotropic materials as well as cracked
and uncracked solids are considered. The focus is on the combined use
the hierarchical representation of the boundary element collocation matrix
and iterative solution procedures. The hierarchical representation of
the collocation matrix is built starting from the generation of the cluster
and block trees that take into account the nature of the considered problem,
i.e. the possible presence of a crack. Low rank blocks are generated
through adaptive cross approximation (ACA) algorithms and the final
hierarchical matrix is further coarsened through suitable procedures also
used for the generation of a coarse preconditioner, which is built taking
full advantage of the hierarchical format. The final system is solved
using a GMRES iterative solver. Applications show that the technique
allows considerable savings in terms of storage memory, assembly time
and solution time without accuracy penalties. Such features make the
method appealing for large scale applications
