Broadband Analysis of Multiscale Electromagnetic Problems: Novel Incomplete-Leaf MLFMA for Potential Integral Equations

Khalichi, Bahram
Ergül, Özgür Salih
Takrimi, Manouchehr
Erturk, Vakur B.
Recently introduced incomplete tree structures for the magnetic-field integral equation are modified and used in conjunction with the mixed-form multilevel fast multipole algorithm (MLFMA) to employ a novel broadband incomplete-leaf MLFMA (IL-MLFMA) to the solution of potential integral equations (PIEs) for scattering/radiation from multiscale open and closed surfaces. This population-based algorithm deploys a nonuniform clustering that enables to use deep levels safely and, when necessary, without compromising the accuracy resulting in an improved efficiency and a significant reduction for the memory requirements (order of magnitudes), while the error is controllable. The superiority of the algorithm is demonstrated in several canonical and real-life multiscale geometries.


Broadband Multilevel Fast Multipole Algorithm Based on an Approximate Diagonalization of the Green's Function
Ergül, Özgür Salih (2015-07-01)
We present a broadband multilevel fast multipole algorithm (MLFMA) for fast and efficient solutions of three-dimensional multiscale problems involving large objects with dense discretizations. The proposed solver is based on the approximate diagonalization of the Green's function using scaled spherical and plane waves, leading to stable interaction computations for arbitrarily short distances in terms of wavelength. Despite contradictory requirements on the scaling factor that limit the accuracy of the diag...
Broadband solutions of potential integral equations with NSPWMLFMA
Khalichi, Bahram; Ergül, Özgür Salih; Ertürk, Vakur B. (Institute of Electrical and Electronics Engineers (IEEE), 2019-06)
In this communication, a mixed-form multilevel fast multipole algorithm (MLFMA) is combined with the recently introduced potential integral equations (PIEs), also called as the A-phi system, to obtain an efficient and accurate broadband solver that can be used for the solution of electromagnetic scattering from perfectly conducting surfaces over a wide frequency range including low frequencies. The mixed-form MLFMA uses the nondirective stable planewave MLFMA (NSPWMLFMA) at low frequencies and the conventio...
Incomplete-Leaf Multilevel Fast Multipole Algorithm for Multiscale Penetrable Objects Formulated With Volume Integral Equations
Takrimi, Manouchehr; Ergül, Özgür Salih; ERTÜRK, VAKUR BEHÇET (2017-09-01)
Recently introduced incomplete-leaf (IL) tree structures for multilevel fast multipole algorithm (referred to as IL-MLFMA) is proposed for the analysis of multiscale inhomogeneous penetrable objects, in which there are multiple orders of magnitude differences among the mesh sizes. Considering a maximum Schaubert-Wilton-Glisson function population threshold per box, only overcrowded boxes are recursively divided into proper smaller boxes, leading to IL tree structures consisting of variable box sizes. Such a...
Rigorous Analysis of Double-Negative Materials with the Multilevel Fast Multipole Algorithm
Ergül, Özgür Salih (2012-02-01)
We present rigorous analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). Accuracy and efficiency of numerical solutions are investigated when DNMs are formulated with two recently developed formulations, i.e., the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCHE). Simulation results on canonical objects are consistent with previous results in the literature on ordin...
Ergül, Özgür Salih (2013-11-09)
A parallel implementation of the multilevel fast multipole algorithm (MLFMA) is developed for fast and accurate solutions of electromagnetics problems involving complex plasmonic metamaterial structures. Composite objects that consist of multiple penetrable regions, such as dielectric, lossy, and plasmonic parts, are formulated rigorously with surface integral equations and solved iteratively via MLFMA. Using the hierarchical strategy for the parallelization, the developed implementation is capable of simul...
Citation Formats
B. Khalichi, Ö. S. Ergül, M. Takrimi, and V. B. Erturk, “Broadband Analysis of Multiscale Electromagnetic Problems: Novel Incomplete-Leaf MLFMA for Potential Integral Equations,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, vol. 69, no. 12, pp. 9032–9037, 2021, Accessed: 00, 2022. [Online]. Available: