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The numerical solution of the helmholtz equation for wave propagation problems in underwater acoustics
| Content Provider | NASA Technical Reports Server (NTRS) |
|---|---|
| Author | Goldstein, C. I. Bayliss, A. Turkel, E. |
| Copyright Year | 1984 |
| Description | The Helmholtz Equation (-delta-K(2)n(2))u=0 with a variable index of refraction, n, and a suitable radiation condition at infinity serves as a model for a wide variety of wave propagation problems. A numerical algorithm was developed and a computer code implemented that can effectively solve this equation in the intermediate frequency range. The equation is discretized using the finite element method, thus allowing for the modeling of complicated geometrices (including interfaces) and complicated boundary conditions. A global radiation boundary condition is imposed at the far field boundary that is exact for an arbitrary number of propagating modes. The resulting large, non-selfadjoint system of linear equations with indefinite symmetric part is solved using the preconditioned conjugate gradient method applied to the normal equations. A new preconditioner is developed based on the multigrid method. This preconditioner is vectorizable and is extremely effective over a wide range of frequencies provided the number of grid levels is reduced for large frequencies. A heuristic argument is given that indicates the superior convergence properties of this preconditioner. |
| File Size | 951916 |
| Page Count | 31 |
| File Format | |
| Alternate Webpage(s) | http://archive.org/details/NASA_NTRS_Archive_19850003326 |
| Archival Resource Key | ark:/13960/t4rj9905s |
| Language | English |
| Publisher Date | 1984-09-01 |
| Access Restriction | Open |
| Subject Keyword | Numerical Analysis Conjugate Gradient Method Helmholtz Equations Boundary Value Problems Backscattering Acoustic Propagation Boundary Conditions Iteration Convergence Finite Element Method Wave Propagation Problem Solving Computational Grids Underwater Acoustics Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science |
| Content Type | Text |
| Resource Type | Technical Report |
