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FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations
Abstract
In this paper, the finite-difference time-domain (FDTD) method is derived for electromagnetic simulations in media described by the time-fractional (TF) constitutive relations. TF Maxwell’s equations are derived based on these constitutive relations and the Grünwald–Letnikov definition of a fractional derivative. Then the FDTD algorithm, which includes memory effects and energy dissipation of the considered media, is introduced. Finally, one-dimensional signal propagation in such electromagnetic media is considered. The proposed FDTD method is derived based on a discrete approximation of the Grünwald–Letnikov definition of the fractional derivative and evaluated in a code. The stability condition is derived for the proposed FDTD method based on a numerical dispersion relation. The obtained numerical results are compared with the outcomes of reference frequency-domain simulations, proving the accuracy of the proposed approach. However, high spatial resolution is required in order to obtain accurate results. The developed FDTD method is, unfortunately, computation and memory demanding when compared to the ordinary FDTD algorithm.
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Authors (3)
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Jacek Gulgowski
Cite as
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- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/app131910654
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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Applied Sciences-Basel
no. 13,
ISSN: 2076-3417 - Language:
- English
- Publication year:
- 2023
- Bibliographic description:
- Pietruszka P., Stefański T., Gulgowski J.: FDTD Method for Electromagnetic Simulations in Media Described by Time-Fractional Constitutive Relations// Applied Sciences-Basel -Vol. 13,iss. 19 (2023), s.10654-
- DOI:
- Digital Object Identifier (open in new tab) 10.3390/app131910654
- Sources of funding:
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- Free publication
- Verified by:
- Gdańsk University of Technology
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