Incomplete-Leaf Multilevel Fast Multipole Algorithm for Multiscale Penetrable Objects Formulated With Volume Integral Equations

Download
2017-09-01
Takrimi, Manouchehr
Ergül, Özgür Salih
ERTÜRK, VAKUR BEHÇET
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 an approach: 1) significantly reduces the CPU time for near-field calculations regarding overcrowded boxes, resulting a superior efficiency in comparison with the conventional MLFMA where fixed-size boxes are used and 2) effectively reduces the computational error of the conventional MLFMA for multiscale problems, where the protrusion of the basis/testing functions from their respective boxes dramatically impairs the validity of the addition theorem. Moreover, because IL-MLFMA is able to use deep levels safely and without compromising the accuracy, the memory consumption is significantly reduced compared with that of the conventional MLFMA. Several examples are provided to assess the accuracy and the efficiency of IL-MLFMA for multiscale penetrable objects.
IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION

Suggestions

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...
Hierarchical Parallelization of the Multilevel Fast Multipole Algorithm (MLFMA)
Gurel, Levent; Ergül, Özgür Salih (2013-02-01)
Due to its O(NlogN) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unkno...
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...
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...
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
M. Takrimi, Ö. S. Ergül, and V. B. ERTÜRK, “Incomplete-Leaf Multilevel Fast Multipole Algorithm for Multiscale Penetrable Objects Formulated With Volume Integral Equations,” IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, pp. 4914–4918, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47999.