A higher-order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies

Donepudi, K.C.; Jin, Jian‐Ming; Chew, Weng Cho

doi:10.1109/aps.2002.1016723

Cited by 15 publications

(26 citation statements)

References 30 publications

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“…In order to extend the practical applicability of SIE-MoM to larger structures, considerable efforts have been made towards the development of fast, efficient algorithms that can reduce the high costs of MoM in terms of both storage and computer processing time. Specifically, we single out the fast multipole method (FMM) [54] and its variants, the multilevel fast multipole algorithm (MLFMA) [27,28], and the MLFMA combined with the fast Fourier transform (FFT) [30][31][32]. Based on Gegenbauer's addition theorem for the homogeneous Green function, the FMM reduces the computational cost to O(N 3/2 ), whereas its multilevel version achieves O(N log N ) by incorporating plain and adjoint interpolation schemes for the fields.…”

Section: Acceleration Techniquesmentioning

confidence: 99%

“…In this paper, we present a deep review of the effort we have made over the last years extending the SIE-MoM [21,[24][25][26] combined with the most recent advances in spectral acceleration techniques, based on the multilevel fast multipole algorithm (MLFMA) [27][28][29] and the fast Fourier transform (FFT) [30][31][32], for the simulation of realistic large-scale plasmonic systems. This methodology was applied for the solution of problems such as the design of nanoantennas [33,34] and optical wireless interconnects [35].…”

Section: Introductionmentioning

confidence: 99%

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SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Solís¹,

Taboada²,

Landesa³

et al. 2015

PIER

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Abstract-The plasmonic behavior of nanostructured materials has ignited intense research for the fundamental physics of plasmonic structures and their cutting-edge applications concerning the fields of nanoscience and biosensing. The optical response of plasmonic metals is generally well-described by classical Maxwell's Equations (ME). Thus, the understanding of plasmons and the design of plasmonic nanostructures can therefore directly benefit from lastest advances achieved in classic research areas such as computational electromagnetics. In this context, this paper is devoted to review the most recent advances in nanoplasmonic modeling, related with the latest breakthroughs in surface integral equation (SIE) formulations derived from ME. These works have extended the scope of application of Maxwell's Equations, from microwave/milimeter waves to infrared and optical frequency bands, in the emerging fields of nanoscience and medical biosensing.

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Section: Acceleration Techniquesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Solís¹,

Taboada²,

Landesa³

et al. 2015

PIER

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“…The method of moments (MoM) [5,6], the finite difference time domain (FDTD) approach [7,8] and T-matrix method [9], etc., have been developed to solve EM scattering by complex bodies consisting of the bi-isotropic media. When the BI objects are homogeneous or piecewise homogeneous, MoM is preferred because it limits the discretization of the unknown quantities to the surfaces of the objects and the discontinuous interfaces between different materials [10][11][12][13]. Despite this, the computational requirements for MoM solution of this type of problems are still very high.…”

Section: Introductionmentioning

confidence: 99%

Solution to Electromagnetic Scattering by Bi-Isotropic Media Using Multilevel Green's Function Interpolation Method

Shi

Chan²

2009

PIER

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Abstract-In this paper, a multilevel Green's function interpolation method (MLGFIM) is developed to analyze electromagnetic scattering from an arbitrarily shaped three-dimensional objects comprised of both conductor and bi-isotropic media. The field decomposition method is adopted to split the homogeneous bi-isotropic media into two uncoupled isotropic media instead of direct calculation of complicated Green's function in bi-isotropic material. The problem is formulated using the Paggio-Miller-Chang-Harrington-WuTsai (PMCHWT) approach for multiple homogeneous isotropic media and electric field approach for conducting bodies. The resultant integral equations are discretized by the method of moment (MoM) and iteratively solved by MLGFIM. Numerical examples illustrate accuracy of this algorithm and CPU time of O(N log N ) and memory requirement of O(N ).

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“…It is more interested these years both in frequency [3][4][5][6][7][8] and time domains [9], especially for complex radar targets in real time. When the dielectric objects are homogenous or piecewise homogenous, on the bases of the equivalent principle, the method of moments (MoM) is preferred because the problem can be formulated in the terms of surface integrals over the conducting and dielectric surfaces at a few number of unknowns.…”

Section: Introductionmentioning

confidence: 99%

“…However, the MoM usually results in a matrix of very large scale when applied to analyzing electrically large objects. Some fast algorithms, such as the multilevel fast multipole algorithm [3,4], precorrected-FFT algorithm [5], and adaptive integral method [6,7], are popularly employed to accelerate the matrix-vector manipulation. Otherwise, higher-order MoM (HO-MoM) can significantly reduce the number of unknowns, provide great flexibility and need less memory [10].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Scattering by Mixed Conducting/Dielectric Objects Using Higher-Order Mom

Wang¹,

Guan²,

Wang³

et al. 2006

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Abstract-In this paper, the higher order hierarchical basis functions are employed to solve the electric field integral equation for computing electromagnetic scattering from three-dimension bodies comprising both conducting and dielectric objects. In higher-order methods of moments (HO-MoM), the equivalent surface electric and magnetic currents are usually expanded by the same basis functions, which are not appropriate in our problem here. The pointwise orthogonal basis functions respectively for electric and magnetic currents are proposed in our improved HO-MoM. Quadrilateral patches are used in curvilinear geometry modeling since they result in the lowest number of unknowns. Numerical solution procedure is particularly analyzed, and numerical results are given for various structures and compared with other available data lastly.

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A higher-order multilevel fast multipole algorithm for scattering from mixed conducting/dielectric bodies

Cited by 15 publications

References 30 publications

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

SQUEEZING MAXWELL'S EQUATIONS INTO THE NANOSCALE (Invited Paper)

Solution to Electromagnetic Scattering by Bi-Isotropic Media Using Multilevel Green's Function Interpolation Method

Electromagnetic Scattering by Mixed Conducting/Dielectric Objects Using Higher-Order Mom

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