The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips
Abstract The Cauchy method of analytical regularisation, first in full explanation, is used for the modelling of the plane wave scattering by a flat pre‐fractal system of impedance strips. It is based on a modification of the singular integral equation technique and the correct type of inversion for...
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| Format: | Article |
| Language: | English |
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Wiley
2021-08-01
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| Series: | IET Microwaves, Antennas & Propagation |
| Subjects: | |
| Online Access: | https://doi.org/10.1049/mia2.12167 |
| _version_ | 1798025921274314752 |
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| author | George I. Koshovy |
| author_facet | George I. Koshovy |
| author_sort | George I. Koshovy |
| collection | DOAJ |
| description | Abstract The Cauchy method of analytical regularisation, first in full explanation, is used for the modelling of the plane wave scattering by a flat pre‐fractal system of impedance strips. It is based on a modification of the singular integral equation technique and the correct type of inversion formula of the simplest Cauchy singular integral equation. The approach is effective for the plane H‐polarised electromagnetic (or sonic) wave scattering problems. The principle of strict mathematical orderings of the pre‐fractal strip grating deals with a five‐parts class of perfect fractal sets, which is characterised by a variable positive fractal dimension. Considerable attention is devoted to the asymptotic model of the plane wave scattering by a sparsely filled grating, which has an explicit solution. This result is very important for verification of the mathematical models presented and testing of direct numerical methods. The scattered electromagnetic field in the far zone is successfully analysed with the aid of the asymptotic solution derived for electrically narrow strips. |
| first_indexed | 2024-04-11T18:26:43Z |
| format | Article |
| id | doaj.art-a98b15c27dfe4aeda476377f68a7e56f |
| institution | Directory Open Access Journal |
| issn | 1751-8725 1751-8733 |
| language | English |
| last_indexed | 2024-04-11T18:26:43Z |
| publishDate | 2021-08-01 |
| publisher | Wiley |
| record_format | Article |
| series | IET Microwaves, Antennas & Propagation |
| spelling | doaj.art-a98b15c27dfe4aeda476377f68a7e56f2022-12-22T04:09:35ZengWileyIET Microwaves, Antennas & Propagation1751-87251751-87332021-08-0115101310131710.1049/mia2.12167The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance stripsGeorge I. Koshovy0Institute of Radio‐Physics and Electronics National Academy of Sciences of Ukraine Harkiv UkraineAbstract The Cauchy method of analytical regularisation, first in full explanation, is used for the modelling of the plane wave scattering by a flat pre‐fractal system of impedance strips. It is based on a modification of the singular integral equation technique and the correct type of inversion formula of the simplest Cauchy singular integral equation. The approach is effective for the plane H‐polarised electromagnetic (or sonic) wave scattering problems. The principle of strict mathematical orderings of the pre‐fractal strip grating deals with a five‐parts class of perfect fractal sets, which is characterised by a variable positive fractal dimension. Considerable attention is devoted to the asymptotic model of the plane wave scattering by a sparsely filled grating, which has an explicit solution. This result is very important for verification of the mathematical models presented and testing of direct numerical methods. The scattered electromagnetic field in the far zone is successfully analysed with the aid of the asymptotic solution derived for electrically narrow strips.https://doi.org/10.1049/mia2.12167diffraction gratingselectromagnetic fieldselectromagnetic wave polarisationelectromagnetic wave scatteringfractalsintegral equations |
| spellingShingle | George I. Koshovy The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips IET Microwaves, Antennas & Propagation diffraction gratings electromagnetic fields electromagnetic wave polarisation electromagnetic wave scattering fractals integral equations |
| title | The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips |
| title_full | The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips |
| title_fullStr | The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips |
| title_full_unstemmed | The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips |
| title_short | The Cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre‐fractal system of impedance strips |
| title_sort | cauchy method of analytical regularisation in the modelling of plane wave scattering by a flat pre fractal system of impedance strips |
| topic | diffraction gratings electromagnetic fields electromagnetic wave polarisation electromagnetic wave scattering fractals integral equations |
| url | https://doi.org/10.1049/mia2.12167 |
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