Subroutines for Direct Solution of Three-Dimensional Elliptic Equations.

Abstract

This report documents three subroutines for the direct numerical solution of three-dimensional separable elliptic equations. The Buneman method of cyclic reduction and factoralization is applied to first reduce a three-dimensional matrix equation to a series of two-dimensional Helmholtz equations. These two-dimensional equations are then reduced by the same method to a series of one-dimensional tridiagonal systems which can be solved very quickly by Gaussian elimination. Three routines are described :POI3DD, POI3NN, and POI3PP. POI3DD assumes Dirichlet conditions on at least two sets of opposite faces of a rectangular body. POI3NN assumes Neumann condition on a staggered grid on at least two sets of faces. POI3PP assumes periodic conditions on at least 2 sets of faces. On the third set of faces any non-periodic conditions can be prescribed. In addition the routines are written in modular form so that other combinations of boundary conditions are easily adopted.

Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1975
Accession Number
ADA013191

Entities

People

  • Thomas E. Rosmond

Tags

DTIC Thesaurus Topics

  • Bodies
  • Boundaries
  • Elimination
  • Equations
  • Geometric Forms
  • Geometry
  • Helmholtz Equations
  • Mathematics
  • Procedures (Computers)
  • Rectangular Bodies
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

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