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

Selçuk, Gökhun
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.


Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations
Ergül, Özgür Salih (2007-04-01)
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...
Improving the accuracy of the surface integral equations for low-contrast dielectric scatterers
Ergül, Özgür Salih (2007-06-15)
Solutions of scattering problems involving low-contrast dielectric objects are considered by employing surface integral equations. A stabilization procedure based on extracting the non-radiating part of the induced currents is applied so that the remaining radiating currents can be modelled appropriately and the scattered fields from the low-contrast objects can be calculated with improved accuracy. Stabilization is applied to both tangential (T) and normal (N) formulations in order to use the benefits of d...
Hybrid Surface Integral Equations for Optimal Analysis of Perfectly Conducting Bodies
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2015-07-24)
We consider hybrid formulations involving simultaneous applications of the electric-field integral equation (EFIE), the magnetic-field integral equation (MFIE), and the combined-field integral equation (CFIE) for the electromagnetic analysis of three-dimensional conductors with arbitrary geometries. By selecting EFIE, MFIE, and CFIE regions on a given object, and optimizing these regions in accordance with the simulation requirements, one can construct an optimal hybrid-field integral equation (HFIE) that p...
Improving the accuracy of the MFIE with the choice of basis functions
Ergül, Özgür Salih (2004-06-26)
In the method-of-moments (MOM) and the fast-multipole-method (FMM) solutions of the electromagnetic scattering problems modeled by arbitrary planar triangulations, the magnetic-field integral equation (MFIE) can be observed to give less accurate results compared to the electric-field integral equation (EFIE), if the current is expanded with the Rao-Wilton-Glisson (RWG) basis functions. The inaccuracy is more evident for problem geometries with sharp edges or tips. This paper shows that the accuracy of the M...
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....
Citation Formats
G. Selçuk, “Application of nyström method for the solution of time domain electric field integral equation,” Ph.D. - Doctoral Program, Middle East Technical University, 2014.