Application of Nyström method for the solution of time domain electric field integral equation

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Tezin Türü: Doktora

Tezin Yürütüldüğü Kurum: Orta Doğu Teknik Üniversitesi, Mühendislik Fakültesi, Elektrik ve Elektronik Mühendisliği Bölümü, Türkiye

Tezin Onay Tarihi: 2014

Öğrenci: GÖKHUN SELÇUK

Danışman: SEYİT SENCER KOÇ

Özet:

Solution of surface scattering problems with electric field integral equation (EFIE) requires careful treatment of singularities introduced by the 3D dyadic Green’s function when source and observation points are close to each other or coincide. One may either utilize the divergence conforming basis and testing functions to reduce the order of singularity or directly deal with singularities via analytical singularity extraction methods. The latter method is a not a commonly used one although it enables use of less complicated pulse-like basis functions and no attempt is done to apply it in time domain. In this study a new time domain formulation for EFIE is obtained. Self-cell contribution is evaluated by an efficient treatment of hypersingular integrals. By using Hadamard finite part interpretation new formulas are introduced for hypersingular integrals on planar surfaces. Also same interpretation is used to obtain explicit expressions for hypersingular integrals on nonplanar surfaces and these expressions improve the accuracy significantly. Close cell contribution is evaluated by increasing the number of quadrature points and applying interpolation. Explicit marching on in time (MOT) scheme along with new formulation is applied to solve transient scattering from perfectly electric conductor (PEC) surfaces. Agreement with analytical results is obtained.