Computer solution of the scattering problem for a groove in a metallic plane using the modal method
The roots of the complex transcendental equations that result from the application of the modal method to the scattering problem for a metallic groove are obtained iteratively as fixed points of entire functions of the form Fc(z), where c, z ∈ ℂ. Iterations are performed with Fc(z) or an appropriate...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_08981221_v35_n11_p98_Ruedin |
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todo:paper_08981221_v35_n11_p98_Ruedin2023-10-03T15:43:59Z Computer solution of the scattering problem for a groove in a metallic plane using the modal method Ruedin, A.M.C. Skigin, D.C. Vaillancourt, R. Fractals Helmholtz equation Iterative solution of transcendental equations Metallic groove Modal method Scattering problem Convergence of numerical methods Electromagnetic wave scattering Fractals Functions Interpolation Iterative methods Modal analysis Problem solving Helmholtz equation Metallic groove Transcendental equations Computer simulation The roots of the complex transcendental equations that result from the application of the modal method to the scattering problem for a metallic groove are obtained iteratively as fixed points of entire functions of the form Fc(z), where c, z ∈ ℂ. Iterations are performed with Fc(z) or an appropriate branch of its multiple-valued inverse function, that is, zj+1 = Fc(zj) or zj+1 = F-1c(zj), respectively. Since convergence fails near double roots, an insightful study of the problem is made and high-precision solutions near double roots are obtained by interpolation. Examples are given to illustrate the behaviour of the methods in different situations, with a connection to fractal theory. © 1998 Elsevier Science Ltd. All rights reserved. Fil:Ruedin, A.M.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Skigin, D.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_08981221_v35_n11_p98_Ruedin |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Fractals Helmholtz equation Iterative solution of transcendental equations Metallic groove Modal method Scattering problem Convergence of numerical methods Electromagnetic wave scattering Fractals Functions Interpolation Iterative methods Modal analysis Problem solving Helmholtz equation Metallic groove Transcendental equations Computer simulation |
| spellingShingle |
Fractals Helmholtz equation Iterative solution of transcendental equations Metallic groove Modal method Scattering problem Convergence of numerical methods Electromagnetic wave scattering Fractals Functions Interpolation Iterative methods Modal analysis Problem solving Helmholtz equation Metallic groove Transcendental equations Computer simulation Ruedin, A.M.C. Skigin, D.C. Vaillancourt, R. Computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| topic_facet |
Fractals Helmholtz equation Iterative solution of transcendental equations Metallic groove Modal method Scattering problem Convergence of numerical methods Electromagnetic wave scattering Fractals Functions Interpolation Iterative methods Modal analysis Problem solving Helmholtz equation Metallic groove Transcendental equations Computer simulation |
| description |
The roots of the complex transcendental equations that result from the application of the modal method to the scattering problem for a metallic groove are obtained iteratively as fixed points of entire functions of the form Fc(z), where c, z ∈ ℂ. Iterations are performed with Fc(z) or an appropriate branch of its multiple-valued inverse function, that is, zj+1 = Fc(zj) or zj+1 = F-1c(zj), respectively. Since convergence fails near double roots, an insightful study of the problem is made and high-precision solutions near double roots are obtained by interpolation. Examples are given to illustrate the behaviour of the methods in different situations, with a connection to fractal theory. © 1998 Elsevier Science Ltd. All rights reserved. |
| format |
JOUR |
| author |
Ruedin, A.M.C. Skigin, D.C. Vaillancourt, R. |
| author_facet |
Ruedin, A.M.C. Skigin, D.C. Vaillancourt, R. |
| author_sort |
Ruedin, A.M.C. |
| title |
Computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| title_short |
Computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| title_full |
Computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| title_fullStr |
Computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| title_full_unstemmed |
Computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| title_sort |
computer solution of the scattering problem for a groove in a metallic plane using the modal method |
| url |
http://hdl.handle.net/20.500.12110/paper_08981221_v35_n11_p98_Ruedin |
| work_keys_str_mv |
AT ruedinamc computersolutionofthescatteringproblemforagrooveinametallicplaneusingthemodalmethod AT skigindc computersolutionofthescatteringproblemforagrooveinametallicplaneusingthemodalmethod AT vaillancourtr computersolutionofthescatteringproblemforagrooveinametallicplaneusingthemodalmethod |
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1807314483294502912 |