THE USE OF DIRECT METHODS FOR THE SOLUTION OF THE DISCRETE POISSON EQUATION ON NON-RECTANGULAR REGIONS

Abstract

Some direct and iterative schemes are presented for solving a standard finite-difference scheme for Poisson's equation on a two-dimensional bounded region R with Dirichlet conditions specified on the boundary of R. These procedures make use of special-purpose direct methods for solving rectangular Poisson problems. The region is imbedded in a rectangle and a uniform mesh is superimposed on it. The usual five-point Poisson difference operator is applied over the whole rectangle, yielding a block-tridiagonal system of equations.

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Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1970
Accession Number
AD0708690

Entities

People

  • J. A. George

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • Boundaries
  • Boundary Value Problems
  • Coefficients
  • Computations
  • Computer Science
  • Convergence
  • Equations
  • Geometry
  • Iterations
  • Military Research
  • Nuclear Energy
  • Poisson Equation
  • Residuals
  • Two Dimensional
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

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