Incremental spectral preconditioners for sequences of linear systems

A technique suited for the solution of sequences of linear systems is described. This technique is a combination of a low rank update spectral preconditioner and a Krylov solver that computes on the fly approximations of the eigenvectors associated with the smallest eigenvalues. A set of Matlab examples illustrates the behaviour of this technique on academic sparse linear systems and its clear interest is showed in large parallel calculations for electromagnetic simulations. In this latter context, the solution technique enables the reduction of the simulation times by a factor of up to eight; these simulation times previously exceeded several hours of computation on a modern high performance computer.