Preconditioner for a discrete Laplace operator on a condensed grid |
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| Authors: | A M Matsokin |
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| Institution: | 1. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia
2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia
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| Abstract: | In this paper, it is proved that the discrete Laplace operator approximating a Dirichlet boundary value problem for a Poisson equation by a finite element method with piecewise-linear functions on an evenly condensed grid that is topologically equivalent to a rectangular grid (i.e., obtained by shifting the rectangular grid nodes) is equivalent, in the range, to the operator of a 5-point difference scheme on a uniform grid. |
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