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Fast relaxation method for solving the difference problem for the poisson equation on a sequence of grids

✍ Scribed by E.A. Ayrjan; E.P. Zhidkov; B.N. Khoromsky

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
390 KB
Volume
29
Category
Article
ISSN
0010-4655

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✦ Synopsis

A method for accelerating the convergence of iterative processes on a sequence of grids is proposed, which makes use of the decomposition of the difference solution into powers of the discretization step. Approximation solutions from a number of auxiliary grids are extrapolated to the exact solution on the finest grid. In the case of a difference problem for the Poisson equation the error of such extrapolation on the last grid is quickly suppressed by simple iterations due to some smoothness properties of the difference-operator eigenfunctions. The results of numerical experiments are presented which illustrate the high efficiency of the proposed method for solution of the given problem.

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