Investigation of the Numerical Method of Moments for Digital Computer Determination of Green's Functions.

Abstract

The purpose of this report was to determine the feasibility of using the method of weighted residuals to obtain approximations to the discrete Green's function or an analog to it. The methods of Galerkin, collocation, and finite differences were programmed on a CDC 7600 computer in Fortran IV. The resulting program was used to generate the approximate functions for the one and two-dimensional Poisson's equation. The two-dimensional case was restricted to the methods of Galerkin and finite differences on a rectangular body. The approximate Green's functions and analogs were applied to a series of inhomogeneity terms to obtain the approximate solutions. The results were compared to the analytical values at points of interest. The average percent error of the approximate solutions is reported for each case as the number of interior nodes of the mesh was increased. The areas of consideration were: the rate of convergence of the approximate solutions toward the analytical solution, the amount of computer-time required to execute the methods, and the accuracy of the approximate solutions. The results of this study indicate that the Green's functions and analogs obtained are valid approximations to the discrete Green's function itself, with the restrictions that additional calculations may be required in the case of the Galerkin approximations and excessive computer-time may occur for high-accuracy approximations. The finite difference approximations were determined to be the best method to use. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1983
Accession Number
ADA138374

Entities

People

  • R. E. Clapp

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Bodies
  • Computer Programs
  • Computers
  • Convergence
  • Differential Equations
  • Digital Computers
  • Equations
  • Errors
  • Fish
  • Method Of Moments
  • Rectangular Bodies
  • Residuals
  • Simultaneous Equations
  • Two Dimensional
  • Weighting Functions

Readers

  • Approximation Theory.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)