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    Multiresolution discrete finite difference masks for rapid solution approximation of the Poisson's equation

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    Ugail_SKIMA.pdf (908.1Kb)
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    Publication date
    2018
    Author
    Jha, R.K.
    Ugail, Hassan
    Haron, H.
    Iglesias, A.
    Keyword
    Poisson's equation
    Laplace operator
    Averaging
    Finite difference scheme
    Rights
    © 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Peer-Reviewed
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    Abstract
    The Poisson's equation is an essential entity of applied mathematics for modelling many phenomena of importance. They include the theory of gravitation, electromagnetism, fluid flows and geometric design. In this regard, finding efficient solution methods for the Poisson's equation is a significant problem that requires addressing. In this paper, we show how it is possible to generate approximate solutions of the Poisson's equation subject to various boundary conditions. We make use of the discrete finite difference operator, which, in many ways, is similar to the standard finite difference method for numerically solving partial differential equations. Our approach is based upon the Laplacian averaging operator which, as we show, can be elegantly applied over many folds in a computationally efficient manner to obtain a close approximation to the solution of the equation at hand. We compare our method by way of examples with the solutions arising from the analytic variants as well as the numerical variants of the Poisson's equation subject to a given set of boundary conditions. Thus, we show that our method, though simple to implement yet computationally very efficient, is powerful enough to generate approximate solutions of the Poisson's equation.
    URI
    http://hdl.handle.net/10454/16874
    Version
    Accepted manuscript
    Citation
    Jha RK, Ugail H, Haron H et al (2018) Multiresolution discrete finite difference masks for rapid solution approximation of the Poisson's equation. In: 2018 12th International Conference on Software, Knowledge, Information Management & Applications (SKIMA). 3-5 Dec, Phnom Penh. Cambodia.
    Link to publisher’s version
    https://doi.org/10.1109/SKIMA.2018.8631514
    Type
    Conference paper
    Collections
    Engineering and Informatics Publications

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