NONITERATIVE SOLUTION OF A BOUNDARY VALUE PROBLEM OF THE HELMHOLTZ TYPE.

Abstract

A noniterative method for solving difference equations of the Helmholtz type in a discretized rectangular domain with uniform grid spacing is presented. This method is an improvement over existing direct methods for the same problem, in terms of both the accuracy and computer storage required. The scheme involves writing a system of linear algebraic equations in the form of a system of matrix equations, applying an orthogonal transformation to this system, reordering the unknowns of the transformed system, and computing the solution of this system by a simple recursion formula. The efficiency, accuracy, and storage demands of this method are compared with existing numerical schemes for solving the same problem. In extreme cases, the computing effort required by the present scheme is only about 30 percent that of the point successive overrelaxation method. For a system having IxI unknowns, the storage demand is at the most about one/I that of other direct methods. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1969
Accession Number
AD0699547

Entities

People

  • Samuel Y. K. Yee

Organizations

  • Air Force Cambridge Research Laboratories

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Boundaries
  • Boundary Value Problems
  • Computers
  • Difference Equations
  • Differential Equations
  • Efficiency
  • Equations
  • Linear Algebraic Equations
  • Mathematical Analysis
  • Mathematics

Fields of Study

  • Mathematics

Readers

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

Technology Areas

  • Space