Calderon's preconditioning for periodic fast multipole method for elastodynamics in 3D

Abstract

Preconditioning methods based on Calderon's formulae for the periodic fast multipole method for elastodynamics in 3D are investigated. Three different types of formulations are proposed. The first type is a preconditioning just by appropriately ordering the coefficient matrix without multiplying preconditioners. The other two types utilise preconditioners constructed using matrices needed in the main fast multipole method algorithms. We make several numerical experiments with proposed preconditioners to confirm the efficiency of these proposed methods. We also conclude that the preconditioning of the first type is faster with respect to the computational time than other preconditioning methods discussed in this article. © 2012 John Wiley & Sons, Ltd.