Solutions of novel potential-based formulations using the multilevel fast multipole algorithm

Gür, Uğur Meriç
In this thesis, recently introduced potential-based formulations that are based on direct usage of magnetic vector and electric scalar potentials, instead of the equivalent field-based formulations, are investigated. These new potential-based formulations can alleviate the well-known low-frequency breakdowns. Therefore, these formulations can be useful in providing the solution of a plethora of problems in future and emerging technologies that are difficult to analyze via standard solvers. The aim of this thesis is to combine potential formulations with special low-frequency implementations of the multilevel fast multiple algorithm (MLFMA) to tackle with finely discretized problems. Thesis also includes the explanation of low-frequency breakdown mechanisms. In addition to the known breakdown of the electric-field integral equation, a hidden breakdown of the potential integral equations (PIEs) is shown. A remedy with the cost of an additional integral equation is proposed. All explanations for the low-frequency breakdown are supported with numerical results. Among low-frequency stable implementations of MLFMA, two methods are implemented for PIEs. One of them is MLFMA based on multipoles without diagonalization. In this method, classical aggregation, translation, and disaggregation procedures in MLFMA are realized without plane-wave expansion. The other one is recently proposed MLFMA implementation with approximate diagonalization. In this method, diagonalization is realized approximately with scaled spherical and plane waves. Accuracy and efficiency of the implementations are shown with numerical results.


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Ergül, Özgür Salih (2011-11-01)
Fast and accurate solutions of large-scale electromagnetics problems involving homogeneous dielectric objects are considered. Problems are formulated with the electric and magnetic current combined-field integral equation and discretized with the Rao-Wilton-Glisson functions. Solutions are performed iteratively by using the multi-level fast multipole algorithm (MLFMA). For the solution of large-scale problems discretized with millions of unknowns, MLFMA is parallelized on distributed-memory architectures us...
Implementation of the equivalence principle algorithm for potential integral equations
Farshkaran, Ali; Ergül, Özgür Salih; Department of Electrical and Electronics Engineering (2018)
In this thesis, a domain decomposition method based on the Huygens' principle for integral equations is studied. Step-by-step development of equivalence principle algorithm (EPA) is described for solving arbitrary shaped perfect electric conductor (PEC) and penetrable objects. The main advantage of EPA is its efficiency thanks to the enhanced conditioning hence accelerated iterative solutions of the matrix equations derived from discretizations. For further enhancing the efficiency, the multilevel fast mult...
Ergül, Özgür Salih; Gurel, L. (2010-01-01)
We present an iterative inner-outer scheme for the efficient solution of large-scale electromagnetics problems involving perfectly-conducting objects formulated with surface integral equations. Problems are solved by employing the multilevel fast multipole algorithm (MLFMA) on parallel computer systems. In order to construct a robust preconditioner, we develop an approximate MLFMA (AMLFMA) by systematically increasing the efficiency of the ordinary MLFMA. Using a flexible outer solver, iterative MLFMA solut...
The use of curl-conforming basis functions for the magnetic-field integral equation
Ergül, Özgür Salih (2006-07-01)
Divergence-conforming Rao-Wilton-Glisson (RWG) functions are commonly used in integral-equation formulations to model the surface current distributions on planar triangulations. In this paper, a novel implementation of the magnetic-field integral equation (MFIE) employing the curl-conforming (n) over tilde x RWG basis and testing functions is introduced for improved current modelling. Implementation details are outlined in the contexts of the method of moments, the fast multipole method, and the multilevel ...
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 ...
Citation Formats
U. M. Gür, “Solutions of novel potential-based formulations using the multilevel fast multipole algorithm,” M.S. - Master of Science, Middle East Technical University, 2018.