Drop tolerance ILU preconditioners for iterative solution techniques in boundary element analysis

A tolerance preconditioning strategy for accelerating the convergence of iterative methods is tested on algebraic equations resulting from boundary element analysis of continuum structural and thermal response problems. The preconditioners are analogs of the drop tolerance incomplete LU(ILU) preconditioners commonly employed with Krylov methods in the solution of sparse linear systems. In all of the problems considered, preconditioned Krylov iteration is more efficient than a dense direct method, with an advantage that improves with problem size. In some of the problems, the optimal drop tolerance ILU(DTILU) preconditioning keeps more nonzeros than simple diagonal preconditioning, but in orders it reduces to the diagonal. A priori determination of the optimal drop remains an open problem.