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

Abstract

The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The specific problem is discretized with a second-order accurate finite-difference 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 rectangulay 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 significant gain in both storage requirement and arithmetic complexity. (Also cross-referenced as UMIACS-TR-96-95)