IACMM – Israel Association for Computational Methods in Mechanics

Numerical solution of the Helmholtz equation is a challenging computational task, particularly when the wave number is large (high frequency). Recent years have seen great improvements in the finite difference approach to this problem through enhancements of the shifted Laplacian preconditioner, originally introduced in [Bayliss et al., JCP 49:443-457, 1983]. For a recent survey and some new results, see [Erlangga, ACME 15:37-66, 2008]. In some cases, this approach may be difficult to implement due to the fact that each iteration of the solver uses a multigrid solution of the preconditioner. More recently, a new approach, based on an algebraic multilevel preconditioner, was introduced in [Bollhöfer et al., SISC 31:3781-3805, 2009]. This approach uses symmetric maximum weight matchings and an inverse-based pivoting strategy.