TY - JOUR T1 - Efficient Iterative Solution of the Three-Dimensional Helmholtz Equation JF - Journal of Computational Physics Y1 - 1998 A1 - Elman, Howard A1 - O'Leary, Dianne P. AB - We examine preconditioners for the discrete indefinite Helmholtz equation on a three-dimensional box-shaped domain with Sommerfeld-like boundary conditions. The preconditioners are of two types. The first is derived by discretization of a related continuous operator that differs from the original only in its boundary conditions. The second is derived by a block Toeplitz approximation to the descretized problem. The resulting preconditioning matrices allow the use of fast transform methods and differ from the discrete Helmholtz operator by an operator of low rank. We present experimental results demonstrating that when these methods are combined with Krylov subspace iteration, convergence rates depend only mildly on both the wave number and discretization mesh size. In addition, the methods display high efficiencies in an implementation on an IBM SP-2 parallel computer. VL - 142 SN - 0021-9991 UR - http://www.sciencedirect.com/science/article/pii/S0021999198959393 CP - 1 M3 - 10.1006/jcph.1998.5939 ER -