Ahstract: -Wavelets technique is applied for solving of 2D and 3D Dirichlet, Neumann and mix boundary problems. The developed method utilizes Haar or linear Battle-Lemarie wavelets functions and Fredholni integral equations (-or a system of the Fredholm integral equations) of fist kind with smooth or singular kernels and developed new method of "prolonged" boundary conditions. The results of the wavelet technique's using are illustrated by calculations of the scattering pattern by dielectric (-or perfect conducting) cylinder with complicated cross sections, ellipsoid of revolution, perfect conducting screens, single and dual-reflector antennas (both kD E 1 and kD >> 1 regions). The problems of accuracy, choosing auxiliary surfaces are discussed.
In this work we present numerical results for the 2D problem of scattering E polarised whispering-gallery mode from concave convex perfectly conducting boundary. The results were obtained by applying the developed method of currants integral equations (CIE) [6,7] for high frequency domain when the size of the scatterer match is greater than the wave length. We have applied the described procedure in order to find numerical solutions of scattering whispering-gallery mode by concave finite convex boundary as a part of a circular cylinder or part of parabolic cylinder. As incident wave we have considered cylindrical waves from line source and Gauss beam [6] with different effective width. It is shown that we have a complicated process of focusing and oscillating of the beam's reflected field, both cylindrical and Gauss beam incident fields. The distortions of reflected field depend on shape of the boundary and parameters of the incident fields.Keywords: Scattering problem, E polarized whispering-gallery mode, concave boundary, integral equation of the first kind, numerical solution.
ResumenEn este trabajo presentamos resultados numéricos para el problema 2D de modo de galería susurrante E polarizada, de una frontera perfectamente conducente cóncava y convexa. Los resultados fueron obtenidos aplicando el método desarrollado de ecuaciones integrales pasas [6,7] para dominios de alta frecuencia cuando el tamaño de la pareja dispersora es mayor que la longitud de onda. Hemos aplicado el procedimiento descrito con tal de encontrar soluciones numéricas de modo galería susurrante de dispersión por frontera convexa finita cóncava, como parte de un cilindro circular * Russian New University, Radio Street 22, 107005 Moscow, Russia. E-Mail: anioutine@mtu-net.ru. † Russian New University 60-2-94, Novocheremushkinskaya UI 117420 Moscow, Russia. E-Mail: walter@robis.ru.
122A.P. Anyutin -V.I. Stasevich Rev.Mate.Teor.Aplic. (2005) 12(1 & 2) o parte de un cilindro parabólico. Como onda de incidencia hemos considerado ondas cilíndricas de fuente de línea y rayo de Gauss [6] con diferentes anchos efectivos. Se muestra que tenemos un proceso complicado de enfoque y oscilación del campo reflajado del rayo, tanto en el campo de incidencia cilíndrico como con el rayo de Gauss. Las distorsiones del campo reflejado depende en la forma de la frontera y los parámetros de los campos de incidencia.Palabras clave: Problema de dispersión, modo de galería susurrante E polarizada, frontera cóncava, ecuación integral de primer tipo, solución numérica.Mathematics Subject Classification: 34L25, 74S15, 65R20.
An universal modification of the method of discrete sources (MMDS) was applied for solving 2D Dirichlet or Neumann boundary problem when the scatterer's contour is a piece-wise smooth contour. The problems of accuracy, choosing auxiliary contours, stable results, location and type of contour's break points are discussed.Keywords: Modification of the method of discrete sources, piece-wise smooth boundary, accuracy.
ResumenUna modificación universal al método de fuentes discretas (MMDS) ha sido aplicada para resolver problemas 2D de frontera de Dirichlet o Neumann cuando el contorno del dispersador es un contorno suave a trazos. Se discuten los problemas de precisión, escogiendo contornos auxiliares, resultados estables, localización y tipo de contorno en los puntos de quiebre.Palabras clave: Modificación del método de fuentes discretas, frontera suave a trozos, precisión.Mathematics Subject Classification: 34L25, 74S15, 65R20.
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