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.
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.