Parallel sparse approximate preconditioners applied to the solution of BEM systems

Engineering problems, such as those dealing with boundary element methods (BEM), usually involve high computational costs. Previous works have proposed effective parallel implementations of BEM. These works have proved the benefit of using parallel computers to solve large civil engineering problems. Despite the profits of the parallel implementation in the discretization step of these methods, the drawback remains the solution of the systems of equations obtained. Because of their fully populated coefficient matrices, direct methods are usually preferable to solve these linear systems. However, parallel implementations of iterative methods achieve higher efficiency, but need suitable preconditioners in order to speed up their convergence. The aim of this work is the research into parallel Sparse Approximate Inverse Preconditioners (SPAI) for the iterative solution of dense systems of equations arising from the boundary element codes. Different heuristics for the construction of SPAI preconditioners suitable for this kind of systems are proposed. Some experiments and numerical results, on distributed-memory computers, are presented in this paper. [Copyright &y& Elsevier]