Numerical Methods for Underwater Structural Acoustics Simulations

摘要

Algorithms were developed for the numerical solution of the Helmholtz problemswith Sommerfeld like boundary conditions. Discretization by finite differences or finite elements can be effectively preconditioned using similar operators but separable boundary condition. We empirically demonstrated that the preconditioners are easy to apply and cause iterative methods such as GMRES to converge in a very modest number of iterations. Parallel implementation on the SP-2 computer enabled efficient solution of quite large problems. We then provided the fast analysis of such problems by noticing that the eigenvalues for two and three-dimensional domains can be calculated exactly by solving a set of one-dimensional eigenvalue problems. This observation permits analysis of quite large problems. Preconditioning using Neumann boundary conditions yields eigenvalues that are uniformly bounded, located in the first quadrant, and outside the unit circle. In contrast, Dirichlet boundary conditions yield eigenvalues that approach zero as the product of wave number with the mesh size is deceased. We have extended our algorithm to inhomogeneous media in which the speed of wave propagation is different on an interior domain. The algorithms display efficiency comparable to that for the homogeneous medium, mating them quite useful for the problem of acoustic analysis with a submarine.