TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions
The analysis of the TM electromagnetic scattering from perfectly electrically conducting polygonal cross-section cylinders is successfully carried out by means of an electric field integral equation formulation in the spectral domain and the method of analytical preconditioning which leads to a matr...
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| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2019/7902836 |
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| author | Mario Lucido Chiara Santomassimo Fulvio Schettino Marco Donald Migliore Daniele Pinchera Gaetano Panariello |
| author_facet | Mario Lucido Chiara Santomassimo Fulvio Schettino Marco Donald Migliore Daniele Pinchera Gaetano Panariello |
| author_sort | Mario Lucido |
| collection | DOAJ |
| description | The analysis of the TM electromagnetic scattering from perfectly electrically conducting polygonal cross-section cylinders is successfully carried out by means of an electric field integral equation formulation in the spectral domain and the method of analytical preconditioning which leads to a matrix equation at which Fredholm’s theory can be applied. Hence, the convergence of the discretization scheme is guaranteed. Unfortunately, the matrix coefficients are improper integrals involving oscillating and, in the worst cases, slowly decaying functions. Moreover, the classical analytical asymptotic acceleration technique leads to faster decaying integrands without overcoming the most important problem of their oscillating nature. Thus, the computation time rapidly increases as higher is the accuracy required for the solution. The aim of this paper is to show a new analytical technique for the efficient evaluation of such kind of integrals even when high accuracy is required for the solution. |
| format | Article |
| id | doaj-art-6b014ac58026457c80d64f42956ab248 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-6b014ac58026457c80d64f42956ab2482025-02-03T01:28:15ZengWileyAdvances in Mathematical Physics1687-91201687-91392019-01-01201910.1155/2019/79028367902836TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying FunctionsMario Lucido0Chiara Santomassimo1Fulvio Schettino2Marco Donald Migliore3Daniele Pinchera4Gaetano Panariello5D.I.E.I. and ELEDIA Research Center (ELEDIA@UniCAS), University of Cassino and Southern Lazio, 03043, Cassino, ItalyD.I.E.I. and ELEDIA Research Center (ELEDIA@UniCAS), University of Cassino and Southern Lazio, 03043, Cassino, ItalyD.I.E.I. and ELEDIA Research Center (ELEDIA@UniCAS), University of Cassino and Southern Lazio, 03043, Cassino, ItalyD.I.E.I. and ELEDIA Research Center (ELEDIA@UniCAS), University of Cassino and Southern Lazio, 03043, Cassino, ItalyD.I.E.I. and ELEDIA Research Center (ELEDIA@UniCAS), University of Cassino and Southern Lazio, 03043, Cassino, ItalyD.I.E.I. and ELEDIA Research Center (ELEDIA@UniCAS), University of Cassino and Southern Lazio, 03043, Cassino, ItalyThe analysis of the TM electromagnetic scattering from perfectly electrically conducting polygonal cross-section cylinders is successfully carried out by means of an electric field integral equation formulation in the spectral domain and the method of analytical preconditioning which leads to a matrix equation at which Fredholm’s theory can be applied. Hence, the convergence of the discretization scheme is guaranteed. Unfortunately, the matrix coefficients are improper integrals involving oscillating and, in the worst cases, slowly decaying functions. Moreover, the classical analytical asymptotic acceleration technique leads to faster decaying integrands without overcoming the most important problem of their oscillating nature. Thus, the computation time rapidly increases as higher is the accuracy required for the solution. The aim of this paper is to show a new analytical technique for the efficient evaluation of such kind of integrals even when high accuracy is required for the solution.http://dx.doi.org/10.1155/2019/7902836 |
| spellingShingle | Mario Lucido Chiara Santomassimo Fulvio Schettino Marco Donald Migliore Daniele Pinchera Gaetano Panariello TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions Advances in Mathematical Physics |
| title | TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions |
| title_full | TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions |
| title_fullStr | TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions |
| title_full_unstemmed | TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions |
| title_short | TM Electromagnetic Scattering from PEC Polygonal Cross-Section Cylinders: A New Analytical Approach for the Efficient Evaluation of Improper Integrals Involving Oscillating and Slowly Decaying Functions |
| title_sort | tm electromagnetic scattering from pec polygonal cross section cylinders a new analytical approach for the efficient evaluation of improper integrals involving oscillating and slowly decaying functions |
| url | http://dx.doi.org/10.1155/2019/7902836 |
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