Abstract
This paper is devoted to increasing the computational efficiency of the finite-difference methods for solving the one-way Helmholtz equation in unbounded domains. The higher-order rational approximation of the propagation operator was taken as a basis. Computation of appropriate approximation coefficients and grid sizes is formulated as the problem of minimizing the discrete dispersion relation error. Keeping in mind the complexity of the developed optimization problem, the differential evolution method was used to tackle it. The proposed method does not require manual selection of the artificial parameters of the numerical scheme. The stability of the scheme is provided by an additional constraint of the optimization problem. A comparison with the Padé approximation method and rational interpolation is carried out. The effectiveness of the proposed approach is shown.
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This study was supported by the Russian Science Foundation grant No. 21-71-00039.
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Lytaev, M.S. (2022). Numerical Approximation of the One-Way Helmholtz Equation Using the Differential Evolution Method. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13350. Springer, Cham. https://doi.org/10.1007/978-3-031-08751-6_15
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