On the errors arising in surface integral equations due to the discretization of the identity operatort

Surface integral equations (SIEs) are commonly used to formulate scattering and radiation problems involving three-dimensional metallic and homogeneous dielectric objects with arbitrary shapes. For numerical solutions, equivalent electric and/or magnetic currents defined on surfaces are discretized and expanded in a series of basis functions. Then, the boundary conditions are tested on surfaces via a set of testing functions. Solutions of the resulting dense matrix equations provide the expansion coefficients of the equivalent currents, which can be used to compute the scattered or radiated electromagnetic fields. This study consists of two parts. In the first part, the authors show that the identity operator is truly a major error source in normal and mixed formulations that are discretized with low-order functions, e.g., Rao-Wilton-Glisson (RWG) functions. In the second part, the authors investigate the incompatibility of SIE formulations in the context of iterative solutions. The authors show that a compatibility test can be used to determine the breakpoint, where the accuracy of the solution is saturated and cannot be enhanced any more.


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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 CFIE-EFIE solution of composite geometries with coexisting open and closed surfaces
Ergül, Özgür Salih (2005-07-08)
The combined-field integral equation (CFIE) is employed to formulate the electromagnetic scattering and radiation problems of composite geometries with coexisting open and closed conducting surfaces. Conventional formulations of these problems with the electric-field integral equation (EFIE) lead to inefficient solutions due to the ill-conditioning of the matrix equations and the internal-resonance problems. The hybrid CFIE-EFIE technique introduced in this paper, based on the application of the CRE on the ...
Fast and accurate solutions of scattering problems involving dielectric objects with moderate and low contrasts
Ergül, Özgür Salih (2007-08-31)
We consider the solution of electromagnetic scattering problems involving relatively large dielectric objects with moderate and low contrasts. Three-dimensional objects are discretized with Rao-Wilton-Glisson functions and the scattering problems are formulated with surface integral equations. The resulting dense matrix equations are solved iteratively by employing the multilevel fast multipole algorithm. We compare the accuracy and efficiency of the results obtained by employing various integral equations ...
On the Accuracy and Efficiency of Surface Formulations in Fast Analysis of Plasmonic Structures via MLFMA
Karaosmanoglu, B.; Yılmaz, Ayşen; Ergül, Özgür Salih (2016-08-11)
We consider the accuracy and efficiency of surface integral equations, when they are used to formulate electromagnetic problems involving plasmonic objects at optical frequencies. Investigations on the iterative solutions of scattering problems with the multilevel fast multipole algorithm show that the conventional formulations, especially the state-of-the-art integral equations, can significantly be inaccurate, in contrast to their performances for ordinary dielectrics. The varying performances of the form...
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...
Citation Formats
Ö. S. Ergül, “On the errors arising in surface integral equations due to the discretization of the identity operatort,” 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/44325.