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This article is cited in 2 scientific papers (total in 2 papers)
Numerical solution of the Poisson equation in polar coordinates by the method of collocations and least residuals
E. V. Vorozhtsova, V. P. Shapeevab a Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch of the Russian Academy of Sciences,
Institutskaya str., 4/1, Novosibirsk, 630090, Russia
b Novosibirsk National Research University,
Pirogov str., 2, Novosibirsk, 630090, Russia
Abstract:
A version of the method of collocations and least residuals is proposed for the numerical solution of the Poisson equation in polar coordinates on non-uniform grids. By introducing general curvilinear coordinates the original Poisson equation is reduced to the Beltrami equation. A uniform grid is used in curvilinear coordinates. The grid non-uniformity in the plane of the original polar coordinates is ensured with the aid of functions which control the grid stretching and entering the formulas of the passage from polar coordinates to the curvilinear ones. The method was verified on two test problems having exact analytic solutions. The examples of numerical computations show that if the radial coordinate axis origin lies outside the computational region, the proposed method has the second order of accuracy. If the computational region contains the singularity, the application of a non-uniform grid along the radial coordinate enables an increase in the numerical solution accuracy by factors from 1.7 to 5 in comparison with the uniform grid case at the same number of grid nodes.
Keywords:
Poisson equation, polar coordinates, the method of collocations and least residuals.
Received: 16.08.2015
Citation:
E. V. Vorozhtsov, V. P. Shapeev, “Numerical solution of the Poisson equation in polar coordinates by the method of collocations and least residuals”, Model. Anal. Inform. Sist., 22:5 (2015), 648–664
Linking options:
https://www.mathnet.ru/eng/mais465 https://www.mathnet.ru/eng/mais/v22/i5/p648
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