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- Title
On the Application of Fractional Derivative Operator Theory to the Electromagnetic Modeling of Frequency Dispersive Media.
- Authors
Deogan, Aneesh S.; Dilz, Roeland; Caratelli, Diego
- Abstract
Fractional derivative operators are finding applications in a wide variety of fields with their ability to better model certain phenomena exhibiting spatial and temporal nonlocality. One area in which these operators are applicable is in the field of electromagnetism, thereby modelling transient wave propagation in complex media. To apply fractional derivative operators to electromagnetic problems, the operator must adhere to certain principles, like the trigonometric functions invariance property. The Grünwald–Letnikov and Marchaud fractional derivative operators comply with these principles and therefore could be applied. The fractional derivative arises when modelling frequency-dispersive dielectric media. The time-domain convolution integral in the relation between the electric displacement and the polarisation density, containing an empirical extension of the Debye model, is approximated directly. A common approach is to recursively update the convolution integral by approximating the time series by a truncated sum of decaying exponentials, with the coefficients found through means of optimisation or fitting. The finite-difference time-domain schemes using this approach have shown to be more computationally efficient compared to other approaches using auxiliary differential equation methods.
- Subjects
OPERATOR theory; COMPUTATIONAL electromagnetics; ELECTROMAGNETIC theory; ELECTRIC displacement; MODEL theory; FINITE difference time domain method
- Publication
Mathematics (2227-7390), 2024, Vol 12, Issue 7, p932
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math12070932