Some Computational Results of an Improved A.D.I. Method for the Dirichlet Problem
Open Access
- 1 November 1966
- journal article
- Published by Oxford University Press (OUP) in The Computer Journal
- Vol. 9 (3) , 298-303
- https://doi.org/10.1093/comjnl/9.3.298
Abstract
The alternating direction implicit (A.D.I.) method of the present authors (Mitchell and Fairweather, 1964) is modified and used to solve the nine-point Laplace difference equation in a square. The greater accuracy of the method, h4 as compared with h2 for the Peaceman–Rachford method, where h is the mesh size, is achieved with no appreciable increase in time or effort. The new A.D.I. method is then combined with the Schwarz Alternating Procedure to solve the nine-point difference equation in non-rectangular regions with sides parallel to the co-ordinate axes. Special attention is given to the re-entrant L-shaped region.Keywords
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