Generalized Shifted Laplace Preconditioner for the High-Frequency Acoustic Scattering Problem

The iterative solution of linear systems arising from wave scattering is a difficult and challenging problem, especially in the high frequency regime.Over the last two decades many preconditioning techniques have been proposed to improve the convergence of iterative solvers; one of the most successful being the Shifted Laplace Preconditioner.The aim of this paper is to propose a generalization of the Shifted Laplace Preconditioner by using operator representation combined with complex Padé approximants.The resulting method is a family of Generalized Shifted Laplace Preconditioners and provides promising results for two-and three-dimensional scattering problems, and that it leads to convergence rates that are weakly frequency-dependent.In the symbolic calculus of pseudodifferential operators, the lowest order member of this new family of preconditioners corresponds to the standard Shifted Laplace Preconditioner.