Title: A phase velocity preserving fourth-order finite difference scheme for the Helmholtz equation with variable wavenumber
Abstract: Numerically solving the Helmholtz equation with large wavenumbers can be challenging due to the highly oscillatory nature of the solution. This paper proposes a 3-point finite difference scheme for numerically solving the 1D Helmholtz equation with variable wavenumber. The proposed scheme preserves the phase velocity, making it well-suited for problems with large wavenumbers. Convergence analysis shows that the proposed scheme is guaranteed to have fourth-order accuracy. Numerical results demonstrate that the proposed scheme maintains high accuracy even for problems with large wavenumbers.
Publication Year: 2024
Publication Date: 2024-04-12
Language: en
Type: article
Indexed In: ['crossref']
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