On the Computationally Efficient Numerical Solution to the Helmholtz Equation

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.

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APA

David, A (2024). On the Computationally Efficient Numerical Solution to the Helmholtz Equation. Afribary. Retrieved from https://afribary.com/works/on-the-computationally-efficient-numerical-solution-to-the-helmholtz-equation

MLA 8th

David, Angwenyi "On the Computationally Efficient Numerical Solution to the Helmholtz Equation" Afribary. Afribary, 04 Jun. 2024, https://afribary.com/works/on-the-computationally-efficient-numerical-solution-to-the-helmholtz-equation. Accessed 06 Jan. 2026.

MLA7

David, Angwenyi . "On the Computationally Efficient Numerical Solution to the Helmholtz Equation". Afribary, Afribary, 04 Jun. 2024. Web. 06 Jan. 2026. < https://afribary.com/works/on-the-computationally-efficient-numerical-solution-to-the-helmholtz-equation >.

Chicago

David, Angwenyi . "On the Computationally Efficient Numerical Solution to the Helmholtz Equation" Afribary (2024). Accessed January 06, 2026. https://afribary.com/works/on-the-computationally-efficient-numerical-solution-to-the-helmholtz-equation

On the Computationally Efficient Numerical Solution to the Helmholtz Equation

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