A fast algorithm for fractional Helmholtz equation with application to electromagnetic waves propagation

Nikita S. Belevtsov and Stanislav Yu. Lukashchuk

Applied Mathematics and Computation, 2022, vol. 416, issue C

Abstract: A fractional Helmholtz equation with the fractional Laplacian is investigated. Fundamental solutions of this equation and their factorized representations in terms of H-functions are constructed using Fourier and Mellin integral transforms. Multipole expansion for integral representation of the fractional Helmholtz equation’s solution is derived. A technique for evaluating H-functions from the multipole expansion is proposed. A modification of the multipole method for solving considered equation is developed. Numerical results demonstrating high efficiency of the proposed approach are presented. A fractional generalization of the mathematical model for a plane polarized electromagnetic wave propagation in the inhomogeneous medium, leading to a fractional Helmholtz equation with the fractional Laplacian, is derived and investigated using the proposed algorithm.

Keywords: Fractional Laplacian; Fractional Helmholtz equation; Multipole expansion; Multipole method; Plane polarized electromagnetic wave propagation (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:416:y:2022:i:c:s0096300321008109

DOI: 10.1016/j.amc.2021.126728

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