Fast-Multipole-Method Solutions of New Potential Integral Equations

Date

2017-09-27

Author

Gür, Uğur Meriç
Karaosmanoglu, Bariscan
Ergül, Özgür Salih

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

132
views

0
downloads

A recently introduced potential integral equations for stable analysis of low-frequency problems involving dense discretizations with respect to wavelength are solved by using the fast multipole method (FMM). Two different implementations of FMM based on multipoles and an approximate diagonalization employing scaled plane waves are developed and used for rigorous solutions of low-frequency problems. Numerical results on canonical problems demonstrate excellent stability and solution capabilities of both implementations.

Subject Keywords

Scattering, Potential integral equations, Low-frequency problems, Fast multipole method

URI

https://hdl.handle.net/11511/54193

Collections

Department of Electrical and Electronics Engineering, Conference / Seminar

Suggestions

OpenMETU
Core

Efficient preconditioning strategies for the multilevel fast multipole algorithm Gurel, Levent; Malas, Tahir; Ergül, Özgür Salih (2007-03-30) For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of MLFMA with the help of the flexible solvers. Among fixed preconditioners, we show that an incomplete LU precondition...
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...
Modified Superformula Contours Optimized via Genetic Algorithms for Exponentially Converging 2D Solutions of MFIE Guler, Sadri; Onol, Can; Ergül, Özgür Salih; Sever, Emrah; Dikmen, Fatih; Tuchkin, Yury A. (2017-05-25) An infinitely smooth parametrical representation with derivatives of all orders is used, resulting into exponentially converging solutions of magnetic field integral equation (MFIE) in 2D either for TM or TE polarized excitations. A version of superformula modified for this purpose has been subject to optimization of its parameters via genetic algorithms to provide smooth parameterization for a desired boundary in two-dimensional problems. The organization of the MFIE kernel and convergence of the solution ...
Rigorous Solutions of Electromagnetic Problems Involving Hundreds of Millions of Unknowns Ergül, Özgür Salih (2011-02-01) Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be easily achieved, even when using the most powerful computers with state-of-the-art technology. Hence, many electromagnetic problems in the literature have been solved by resorting to various approximation techniques, without controllable error. In this paper, we present full-wave solutions of sc...
On the accuracy of MFIE and CFIE in the solution of large electromagnetic scattering problems Ergül, Özgür Salih (null; 2006-11-10) 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 large scatterers. MFIE and CFIE with the conventional Rao-Wilton-Glisson (RWG) basis functions are significantly inaccurate even for large and smooth geometries, such as a sphere, compared to the solutions by the electric-field integral equation (EFIE). By using the LL funct...

Citation Formats

U. M. Gür, B. Karaosmanoglu, and Ö. S. Ergül, “Fast-Multipole-Method Solutions of New Potential Integral Equations,” 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54193.