Application of two-grid interpolation to enhance average gradient method for solving partial differential equations
Pohjonen, Aarne
Institute of physics publishing
Aarne Pohjonen 2024 J. Phys.: Conf. Ser. 2701 012103, doi: 10.1088/1742-6596/2701/1/012103
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Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.
https://creativecommons.org/licenses/by/3.0/
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Published under licence by IOP Publishing Ltd.
https://creativecommons.org/licenses/by/3.0/
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202403122182
https://urn.fi/URN:NBN:fi:oulu-202403122182
Tiivistelmä
Abstract
Previously presented method of calculating local average gradients for solving partial differential equations (PDEs) is enhanced by using interpolating gridpoints and triangular grids. The interpolating mesh provides finer computational grid, which is then used for solving the PDE. The combined use of the finer interpolating grid together with the original sparser grid is a two-grid method. By comparing the previous application of rectilinear grid for diffusion from initial point concentration to the new triangular two grid method, it was found that the application of triangular two-grid method improves stability of the solution and it provides more rapid convergence to the correct analytical solution.
Previously presented method of calculating local average gradients for solving partial differential equations (PDEs) is enhanced by using interpolating gridpoints and triangular grids. The interpolating mesh provides finer computational grid, which is then used for solving the PDE. The combined use of the finer interpolating grid together with the original sparser grid is a two-grid method. By comparing the previous application of rectilinear grid for diffusion from initial point concentration to the new triangular two grid method, it was found that the application of triangular two-grid method improves stability of the solution and it provides more rapid convergence to the correct analytical solution.
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- Avoin saatavuus [37684]
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