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