Abstract
The numerical solution of the Helmholtz equation subject to nonlocal radiation boundary conditions is studied. The specific problem is the propagation of hydroacoustic waves in a two-dimensional curvilinear duct. The 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. We construct a preconditioner that 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. The fast transform preconditioner is compared with a symmetric successive over-relaxation (SSOR) preconditioner, and also with band Gaussian elimination. For the preconditioned iterative methods, the gains in storage requirement are large compared with band Gaussian elimination. Regarding the arithmetic complexity, the fast transform preconditioner yields a significant gain, whereas the SSOR preconditioner performs worse than band Gaussian elimination.
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