BLOCK RELAXATION BY COMPUTER,
Abstract
Let it be required to find the values phi sub i j at grid points, for a grid of squares of side h, of the solution to a difference equation approximation to Laplace's equations in a region, being given values on the boundary. For computer purposes, we define a block relaxation as follows. Given estimates of phi sub i j on the boundary of a block, one determines the solution of the difference equation inside the block for the given values of phi sub i j on its boundary, and takes these as the new estimates for the phi sub i j at points inside the block. One can take the blocks to be squares of side 2Nh, and then the successive relaxations are uniquely determined if estimates for phi sub i j are available only at points of a filagree consisting of the grid points on a network consisting of horizontal and vertical lines which are separated by a distance of Nh . By restricting attention exclusively to filagree points until convergence is complete, the demands on computer memories are reduced by factors as great as eight. This holds out the promise of dealing with problems of a size hitherto unmanageable. The method is easily extended to the solution of Poisson's equation. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1964
- Accession Number
- AD0600740
Entities
People
- J. Barkley Rosser
Organizations
- University of Wisconsin–Madison