We are concerned in this talk with the improvement of the efficiency of iterative solver treating of 3D frequency domain (acoustic and elastic) wave propagation problems through Boundary Element Method (BEM). Since the fundamental solutions involved in the integral equations are of non-local support, the discretization with the BEM yields to some linear systems with fully-populated matrices and therefore memory storage consuming.
$\mathcal{H}$-matrix (Hierarchical matrix) technique offers an alternative data-sparse representation to these matrices. This representation is based on a hierarchical partitioning of the system matrix and the use of low-rank approximations for some blocks which are a priori known as low-rank admissible. We propose an algebraic preconditioner for the $\mathcal{H}$-matrix based iterative solver. The preconditioner is not defined explicitly. Indeed, only its application to a given vector is required and obtained as the solution of a linear system, also computed through an iterative solver. As a result, one deals with a two-level iterative solver. The efficiency of the proposed preconditioner will be shown with some numerical tests. This work is done in collaboration with Stéphanie Chaillat and Patrick Ciarlet.