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    On the Computationally Efficient Numerical Solution to the Helmholtz Equation

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    On the Computationally Efficient Numerical Solution to the Helmholtz Equation.pdf (464.1Kb)
    Date
    2018-02
    Author
    Angwenyi, N. David
    Lawi, George
    Ojiema, Michael
    Owino, Maurice
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    Abstract
    Named after Hermann L. F. von Helmholtz (1821-1894), Helmholtz equation has obtained application in many elds: investigation of acaustic phenomena in aeronautics, electromagnetic application, migration in 3-D geophysical application, among many other areas. As shown in [2], Helmholtz equation is used in weather prediction at the Met O ce in UK. Ine ciency, that is the bottleneck in Numerical Weather Prediction, arise partly from solving of the Helmholtz equation. This study investigates the computationally e cient iterative method for solving the Helmholtz equation. We begin by analysing the condition for stability of Jacobi Iterative method using Von Neumann method. Finally, we conclude that Bi-Conjugate Gradient Stabilised Method is the most computationally e cient method.
    URI
    http://dx.doi.org/10.12988/imf.2014.311224
    http://ir-library.mmust.ac.ke:8080/xmlui/handle/123456789/2848
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