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...
| Autores principales: | , |
|---|---|
| Publicado: |
1998
|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v35_n11_p98_Ruedin http://hdl.handle.net/20.500.12110/paper_08981221_v35_n11_p98_Ruedin |
| Aporte de: |
| id |
paper:paper_08981221_v35_n11_p98_Ruedin |
|---|---|
| record_format |
dspace |
| spelling |
paper:paper_08981221_v35_n11_p98_Ruedin2023-06-08T15:49:23Z Computer solution of the scattering problem for a groove in a metallic plane using the modal method Ruedin, Ana María Clara Skigin, Diana Carina 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. 1998 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v35_n11_p98_Ruedin 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, Ana María Clara Skigin, Diana Carina 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. |
| author |
Ruedin, Ana María Clara Skigin, Diana Carina |
| author_facet |
Ruedin, Ana María Clara Skigin, Diana Carina |
| author_sort |
Ruedin, Ana María Clara |
| 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 |
| publishDate |
1998 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_08981221_v35_n11_p98_Ruedin http://hdl.handle.net/20.500.12110/paper_08981221_v35_n11_p98_Ruedin |
| work_keys_str_mv |
AT ruedinanamariaclara computersolutionofthescatteringproblemforagrooveinametallicplaneusingthemodalmethod AT skigindianacarina computersolutionofthescatteringproblemforagrooveinametallicplaneusingthemodalmethod |
| _version_ |
1768545981214752768 |