New Finite Difference Schemes for Helmholtz Equation
DOI:
https://doi.org/10.35819/remat2024v10iespecialid7019Keywords:
Helmholtz equation, finite difference method, dispersion analysis, pollution error, stabilizationAbstract
The Helmholtz scalar equation describes the temporal harmonics of acoustic waves. It is well known that finite difference and finite element methods exhibit the effect of pollution error for medium and high wavenumber. In this work, three new centered finite difference schemes of second order precision in one and two dimensions are analyzed. These new schemes are consistent, and were obtained by new approximations only on the second term of the Helmholtz equation. Dispersion analysis, error behavior and numerical results show the good performance of New Schemes 2 and 3. New Scheme 3 is able to eliminate the pollution error effect in one dimension and minimize the dispersion of the plane wave in two dimensions.
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