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A Symbolic-Numeric Method for Solving the Poisson Equation in Polar Coordinates

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Computer Algebra in Scientific Computing (CASC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14139))

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Abstract

A new version of the method of collocations and least squares (CLS) is proposed for the numerical solution of the Poisson equation in polar coordinates on uniform and non-uniform grids. To increase the accuracy of the numerical solution the degree of the local approximating polynomial has been increased by one in comparison with the earlier second-degree version of the CLS method for solving the Poisson equation. By introducing the general curvilinear coordinates the original Poisson equation has been reduced to the Beltrami equation. The method has been verified on three test problems having the exact analytic solutions. The examples of numerical computations show that if the singularity – the radial coordinate origin lies outside the computational region then the proposed method produces the solution errors which are two orders of magnitude less than in the case of the earlier CLS method. If the computational region contains the singularity then the solution errors are generally two and three orders of magnitude less than in the case of a second-degree approximating polynomial at the same number of grid nodes.

The research was carried out within the state assignment of Ministry of Science and Higher Education of the Russian Federation.

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Authors and Affiliations

  1. Khristianovich Institute of Theoretical and Applied Mechanics of the Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia

    Evgenii V. Vorozhtsov

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  1. Evgenii V. Vorozhtsov
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Correspondence to Evgenii V. Vorozhtsov .

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Editors and Affiliations

  1. University of Lille, CRIStAL, Villeneuve d'Ascq, France

    François Boulier

  2. Coventry University, Coventry, UK

    Matthew England

  3. Wilfrid Laurier University, Waterloo, ON, Canada

    Ilias Kotsireas

  4. Plekhanov Russian University of Economics, Moscow, Russia

    Timur M. Sadykov

  5. Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia

    Evgenii V. Vorozhtsov

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Vorozhtsov, E.V. (2023). A Symbolic-Numeric Method for Solving the Poisson Equation in Polar Coordinates. In: Boulier, F., England, M., Kotsireas, I., Sadykov, T.M., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2023. Lecture Notes in Computer Science, vol 14139. Springer, Cham. https://doi.org/10.1007/978-3-031-41724-5_18

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  • DOI: https://doi.org/10.1007/978-3-031-41724-5_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-41723-8

  • Online ISBN: 978-3-031-41724-5

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