The Numerical Solution of Underwater Acoustic Propagation Problems Using Finite Difference and Finite Element Methods

Abstract

This report discusses various aspects of the numerical solution of underwater acoustic wave propagation problems. In the first part of the report, a model propagation problem based on the two-dimensional Helmholtz equation with a variable sound speed is considered. A finite element computer code for solving such problems was implemented at NRL on the VAX 11/780. A distinctive feature of the code is the implementation of a recently developed iterative method for solving the resulting large, sparse, indefinite, non-self-adjoint system of equations. This allowed for the efficient solution of over 35,000 complex equations on a relatively small computer. Some of the results obtained after applying this code to the model problem are described. Furthermore, additional modifications that can be made to the code to improve its efficiency and extend its applicability to more general propagation models are discussed. In the second part of this report, the general situation of the coupled acoustic/ elastic wave equation in two and three dimensions is considered. For example, this may correspond to an ocean environment in which there is ice on the surface as well as an irregularly shaped bottom structure. Finite difference and finite element methods for solving both the time harmonic and time dependent models are discussed. Various issues are considered that are important in determining the size of the problem that can be adequately treated. This includes the computer power as well as the mathematical and modeling techniques available.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jul 09, 1984
Accession Number
ADA143968

Entities

People

  • C. I. Goldstein

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustic Propagation
  • Acoustic Waves
  • Acoustics
  • Applied Mathematics
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Differential Equations
  • Elastic Waves
  • Equations
  • Geometry
  • Helmholtz Equations
  • Parallel Computing
  • Partial Differential Equations
  • Refractive Index
  • Two Dimensional
  • Wave Equations

Fields of Study

  • Mathematics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)