Broadband Multilevel Fast Multipole Algorithm Based on an Approximate Diagonalization of the Green's Function

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 diagonalization, the resulting low-frequency scheme is extremely stable and easy to plug into conventional MLFMA implementations by simply extending built-in tree structures, converting them into broadband solvers without needing dense programming efforts. Accuracy and efficiency of the broadband MLFMA are demonstrated on canonical problems, as well as on multiscale problems that cannot be solved efficiently via standard implementations of MLFMA.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION

Suggestions

Broadband Multilevel Fast Multipole Algorithm For Large-Scale Problems With Nonuniform Discretizations
Ergül, Özgür Salih; Takrimi, Manouchehr; Erturk, Vakur B. (2016-08-18)
We present a broadband implementation of the multilevel fast multipole algorithm (MLFMA) for fast and accurate solutions of multiscale problems involving highly nonuniform discretizations. Incomplete tree structures, which are based on population-based clustering with flexible leaf-level boxes at different levels, are used to handle extremely varying triangulation sizes on the same structures. Superior efficiency and accuracy of the developed implementation, in comparison to the standard and broadband MLFMA...
Broadband Analysis of Multiscale Electromagnetic Problems: Novel Incomplete-Leaf MLFMA for Potential Integral Equations
Khalichi, Bahram; Ergül, Özgür Salih; Takrimi, Manouchehr; Erturk, Vakur B. (2021-12-01)
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 compromi...
PARALLEL MULTILEVEL FAST MULTIPOLE ALGORITHM FOR COMPLEX PLASMONIC METAMATERIAL STRUCTURES
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...
Rigorous Solutions of Large-Scale Scattering Problems Discretized with Hundreds of Millions of Unknowns
Guerel, L.; Ergül, Özgür Salih (2009-09-18)
We present fast and accurate solutions of large-scale scattering problems using a parallel implementation of the multilevel fast multipole algorithm (MLFMA). By employing a hierarchical partitioning strategy, MLFMA can be parallelized efficiently on distributed-memory architectures. This way, it becomes possible to solve very large problems discretized with hundreds of millions of unknowns. Effectiveness of the developed simulation environment is demonstrated on various scattering problems involving canonic...
Multifrequency and multidirection optimizations of antenna arrays using heuristic algorithms and the multilevel fast multipole algorithm
Onol, Can; Alkis, Sena; Gokce, Ozer; Ergül, Özgür Salih (2016-07-01)
We consider fast and efficient optimizations of arrays involving three-dimensional antennas with arbitrary shapes and geometries. Heuristic algorithms, particularly genetic algorithms, are used for optimizations, while the required solutions are carried out accurately and efficiently via the multilevel fast multipole algorithm(MLFMA). The superposition principle is employed to reduce the number of MLFMA solutions to the number of array elements per frequency. The developed mechanism is used to optimize arra...
Citation Formats
Ö. S. Ergül, “Broadband Multilevel Fast Multipole Algorithm Based on an Approximate Diagonalization of the Green’s Function,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 3035–3041, 2015, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45092.