Equivalence Principle Algorithm for Potential Integral Equations

Farshkaran, Ali
Ergül, Özgür Salih
We present a new frequency-domain implementation of the equivalence principle algorithm (EPA) using the recently developed potential integral equations (PIEs) as inner formulations. The set of equivalent sources is updated by including all components of electric and magnetic fields, as well as potentials required for PIEs. The developed implementation is stable when applied to challenging problems involving extremely dense discretizations with respect to wavelength, while it is efficient at the same time thanks to the improved iterative solutions using EPA. The accuracy of the implementation is shown for the first time on canonical problems.


Combined Potential-Field Surface Formulations for Resonance-Free and Low-Frequency-Stable Analyses of Three-Dimensional Closed Conductors
Eris, Ozgur; Karaova, Gokhan; Ergül, Özgür Salih (2021-03-22)
We present combined formulations involving the recently developed potential integral equations (PIEs) together with field formulations, particularly the magnetic-field integral equation (MFIE), for accurate, efficient, and stable analyses of three-dimensional closed conductors. This kind of combinations are required since PIEs suffer from internal resonances and are prone to numerical issues for relatively large conductors. By combining PIEs with MFIE, we obtain low-frequency-stable implementations that can...
Analysis of double-negative materials with surface integral equations and the multilevel fast multipole algorithm
Ergül, Özgür Salih (2011-08-13)
We present a fast and accurate analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). DNMs are commonly used as simplified models of metamaterials at resonance frequencies and are suitable to be formulated with surface integral equations. However, realistic metamaterials and their models are usually very large with respect to wavelength and their accurate solutions require fast algorithms, such as MLFMA. We consider iterative solutio...
Generalized Hybrid Surface Integral Equations for Finite Periodic Perfectly Conducting Objects
Karaosmanoglu, Bariscan; Ergül, Özgür Salih (2017-01-01)
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...
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...
Low-frequency Breakdown of the Potential Integral Equations and Its Remedy
Gür, Uğur Meriç; Ergül, Özgür Salih (2017-11-22)
Potential integral equations (PIEs) introduced recently also have a low-frequency breakdown that becomes visible when considering the electric charge density and near-zone electric field intensity values. As opposed to the well-known low-frequency breakdown of the electric-field integral equation (EFIE), which shows itself as both inaccuracy and ill-conditioning, the low-frequency breakdown of PIEs is not related to the conditioning properties of the related matrix equations. Therefore, we clearly distingui...
Citation Formats
A. Farshkaran and Ö. S. Ergül, “Equivalence Principle Algorithm for Potential Integral Equations,” 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38639.