Preconditioning the Helmholtz Equation for a 2-D Duct

A preconditioning technique has been developed for numerical solution of the Helmholtz equation as applied to the steady-state propagation of sound in a semi-infinite, two-dimensional (2-D) rigid duct. As explained below, the technique involves the use of two pseudo-time parameters in a finite-difference approximation of the equation that describes the propagation of sound. The use of these parameters makes the solution proceed much faster than in older transient- and steady-state-analysis-based numerical solution methods.