The Numerical Solution of the Helmholtz Equation for Wave Propagation Problems in Underwater AcousticsNational Aeronautics and Space Administration, Langley Research Center, 1984 - Helmholtz equation - 31 pages |
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analyze convergence arbitrary number backscattering boundary operator coarsest grid conjugate gradient algorithm conjugate gradient method D₁ defined describe Dirichlet boundary condition discrete Laplacian eigenvalues evanescent modes fast Laplace solvers finer grids finite element method fixed prescribed accuracy Furthermore Global 20 global boundary condition global radiation boundary gradient method applied grid levels Helmholtz Equation index of refraction interfaces with strong iterations required iterative method K3h2 fixed K3h2 Iterations Modes in BC multigrid method multigrid preconditioner normal equations number of equations number of grid number of iterations number of levels number of propagating numerical algorithm numerical method numerical results O(K² preconditioned conjugate gradient preconditioners based prescribed accuracy level propagating modes provided the number radiation boundary condition range of frequencies rate greater relaxation sweeps required for convergence Results for Example Section small number SSOR and ADI strong velocity contrasts suitable radiation condition system of linear TABLE vector Wave Propagation Problems