| Abstract: | The convergence behaviour of conjugate direction methods for Helmholtz problems with complex-valued wavenumbers is studied. The model problem is a Galerkin discretization of the scalar Helmholtz equation on square arrays of 2D and 3D, C° linear elements. A series of controlled experiments is performed which use the dimensionless wavenumber and the algebraic size of the system of equations to completely characterize the iterative performance of the solvers. The effects of algebraic size are examined as functions of both mesh refinement and mesh extension within the limits of present-day workstation computing environments. A comparison is drawn between the conjugate direction methods investigated and the equivalent time-domain solution obtained through explicit time-stepping. |
