Electrical - Electronic Engineering / Elektrik - Elektronik Mühendisliği
Permanent URI for this collectionhttps://hdl.handle.net/11147/11
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Article Citation - WoS: 1Citation - Scopus: 1Revised Distributional Forms of the Laplacian and Poisson's Equation, Their Implications, and All Related Generalizations(Taylor and Francis Ltd., 2015) Kuştepeli, AlpThe theory of distributions of L. Schwartz is a very useful and convenient way for the analysis of physical problems since physical distributions, especially charge distributions yielding the discontinuity of the potential and boundary conditions, can be correctly described in terms of mathematical distributions. To obtain the charge distributions, the distributional form of the Laplacian is applied to the Poisson's equation; therefore, for the correct representations and interpretations, the distributional forms and their proper applications are very important. In this article, it is shown that the distributional form of the Laplacian has been presented by Schwartz and also others with a missing term, leading to confusing and wrong results mathematically, and as a result electromagnetically; and the revised, correct, and complete distributional representations of the Laplace operator, the Poisson equation, and double layers, defined as the dipole layer and equidensity layer, are obtained and presented with detailed discussions and explanations including boundary conditions. By using the revised form of the Laplacian, Green's theorem is obtained explicitly with special emphases about important points and differences with previous works. The generalized forms of the Laplacian, Poisson's equation, charge densities, boundary conditions, and Greens theorem are also presented when there is a multi-layer on the surface of discontinuity.Conference Object Citation - Scopus: 1Three-Dimensional Electromagnetic Scattering From Flat Plates by Using Sinc-Type Basis Functions in Method of Moments(Institute of Electrical and Electronics Engineers Inc., 2009) Özbakış, Başak; Oğuzer, Taner; Kuştepeli, AlpSinc functions are used in the basis and testing procedures in the conventional method of moments (MoM) formulation. But unlike conventional MoM, simple pointwise meshing is enough and no integral computation is required due to the mathematical properties of the sinc function. The simulation results of surface current densities and radar cross section for a few wavelength square flat plate are obtained by using our own codes. The results are compared with those of the rooftop basis functions. The CPU-time decreases by half of the time of the conventional method. The error that occurs from the approximated integral of the sinc function in the computation of main matrix elements is very small and decreases while the bandwidth of the sinc function increases.