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Novel Nystrom Method for TDEFIE
Date
2014-04-11
Author
Selcuk, Gokhun
Koç, Seyit Sencer
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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 consult to 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 commonly used 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 efficient treatment of hypersingular integrals and 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 perfect electric conductor (PEC) surfaces. Agreement with analytical results is obtained.
Subject Keywords
MOT scheme
,
Hypersingular integral
,
EFIE
URI
https://hdl.handle.net/11511/54055
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Department of Electrical and Electronics Engineering, Conference / Seminar
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Application of nyström method for the solution of time domain electric field integral equation
Selçuk, Gökhun; Koç, Seyit Sencer; Department of Electrical and Electronics Engineering (2014)
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 ...
Evaluation of Hypersingular Integrals on Non-planar Surfaces
Selcuk, Gokhun; Koç, Seyit Sencer (2014-05-16)
Solving electric field integral equation (EFIE) with Nystrom method requires accurate evaluation of hypersingular surface integrals since this method does not use divergence conforming basis and testing functions. The success of the method also depends on accurate representation of non-planar characteristics of the scattering object. In this study Hadamard finite part interpretation is used to evaluate hypersingular integrals over non-planar surfaces, which are represented by their Taylor series expansions....
Evaluation of Hypersingular Integrals on Curvilinear Surface Elements
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In this study finite part integrals are utilized for evaluation of hypersingular and nearly-hypersingular surface integrals on curvilinear elements. These integrals are related to the second derivative of the free space Green' function and arise in the solution of electric field integral equation (EFIE) via locally corrected Nystriim (LCN) method. The curvilinear elements are represented by the Taylor series expansion of the surface function around the observation point. The hypersingular integral, defined ...
Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations
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We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can...
Generalized Hybrid Surface Integral Equations for Finite Periodic Perfectly Conducting Objects
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Hybrid formulations that are based on simultaneous applications of diversely weighted electric-field integral equation (EFIE) and magnetic-field integral equation (MFIE) on periodic but finite structures involving perfectly conducting surfaces are presented. Formulations are particularly designed for closed conductors by considering the unit cells of periodic structures as sample problems for optimizing EFIE and MFIE weights in selected regions. Three-region hybrid formulations, which are designed by geneti...
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G. Selcuk and S. S. Koç, “Novel Nystrom Method for TDEFIE,” 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54055.
