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

Takrimi, Manouchehr
Ergül, Özgür Salih
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.


Near-Field-Based Preconditioning Technique in the Incomplete-Leaf MLFMA for Nonuniformly Discretized Electromagnetic Scattering Problems
Khalichi, Bahram; Ergül, Özgür Salih; Eruirk, Vakur B. (2021-01-01)
© 2021 IEEE.The potential of incomplete tree structures, previously used in the context of the multilevel fast multi pole algorithm, on developing an effective preconditioning technique for multiscale electromagnetic problems is analyzed. The preconditioning technique is based on the sparse near-field matrix constructed by the near-field clustering definition of the incomplete tree structures for multiscale geometries. The proposed preconditioner is applied to solutions of matrix systems obtained via method...
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)
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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...
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
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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...
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: