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Comparison of some modifications in method of auxiliary sources

Keywords:

A.V. Korobkina – Student, Moscow Institute of Physics and Technology (State University) E-mail: korobkina@phystech.edu S.P. Skobelev – Dr. Sc. (Phys.-Math.), Leading Research Scientist, PJSC «Radiofizika» (Moscow), Associate Professor, Moscow Institute of Physics and Technology (State University) E-mail: s.p.skobelev@mail.ru


Comparison of the effectiveness of a few modifications in the method of auxiliary sources applied for solution of two-dimensional problem of E-polarized plane wave scattering by perfectly conducting cylinders of circular and elliptical cross sections is carried out. The rate of decreasing of the maximum residual of fulfilling the boundary condition down to the machine precision with increasing the number of auxiliary sources is chosen as a criterion. For the case of a circular cylinder, the modification in which the ratio of the distance between the original cylinder and the auxiliary one to the spacing between the collocation points remains constant with increasing the number of the sources is compared to the modification where the distance between the cylinders itself remains constant with increasing the number of sources. It is shown that the maximum effectiveness is provided with using the latter modification. Optimum values for the radius of the auxiliary cylinder are obtained and presented as a function of the radius of the original cylinder. In the case of elliptical cylinder, there has been carried out a comparison between a modification where the auxiliary surface is chosen in the form of elliptical cylinder of the same axial ratio as that in the original one, a modification where the auxiliary surface is an elliptical cylinder confocal to the original one, and a modification where the auxiliary surface is determined as a result of analytical deformation of the original cylinder corresponding to the so-called modified method of discrete sources. For the three modifications indicated above, there have been considered two cases of arrangement of the collocation points and appropriate source points when the points are arranged uniformly over the values of the azimuth angle in the polar coordinate system in the former case and when the points are arranged uniformly over the values of the parameter used in the equations used for representation of the ellipse in parametric form. It is shown that the maximum effectiveness exceeding the effectiveness of the modified method of discrete sources is achieved when a confocal auxiliary elliptical cylinder is used and when the collocation and source points are arranged according to the ellipse equations specified in the parametric form.
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