Iterative Solution of the Helmholtz Equation by a Second-Order Method

The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The speciic problem is the propagation of hydroacoustic waves in a two-dimensional curvilinear duct. The problem is discretized with a second-order accurate nite-diierence method, resulting in a linear system of equations. To solve the system of equations, a preconditioned Krylov subspace method is employed. The preconditioner is based on fast transforms , and yields a direct fast Helmholtz solver for rectangular domains. Numerical experiments for curved ducts demonstrate that the rate of convergence is high. Compared with band Gaussian elimination the preconditioned iterative method shows a signiicant gain in both storage requirement and arithmetic complexity.