The accuracy of fast multipole methods for Maxwell's equations

Dembart, B.; Yip, E. L.

doi:10.1109/99.714593

Cited by 59 publications

(34 citation statements)

References 6 publications

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“…In both cases the FMM was proven to have an asymptotic complexity O(Nln 2 (N)). Application of the FMM to surface-integrals formulation of light scattering was reviewed by Dembart and Yip [132].…”

Section: Fast Multipole Methodsmentioning

confidence: 99%

The discrete dipole approximation: An overview and recent developments

Yurkin

Hoekstra

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

771

458

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We present a review of the discrete dipole approximation (DDA), which is a general method to simulate light scattering by arbitrarily shaped particles. We put the method in historical context and discuss recent developments, taking the viewpoint of a general framework based on the integral equations for the electric field. We review both the theory of the DDA and its numerical aspects, the latter being of critical importance for any practical application of the method. Finally, the position of the DDA among other methods of light scattering simulation is shown and possible future developments are discussed.

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Section: Fast Multipole Methodsmentioning

confidence: 99%

The discrete dipole approximation: An overview and recent developments

Yurkin

Hoekstra

2007

Journal of Quantitative Spectroscopy and Radiative Transfer

771

458

View full text Add to dashboard Cite

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“…However, computations performed using this formulation become unstable for higher levels of refinement with small local Helmholtz numbers. This problem is referred in the literature as subwavelength breakdown, and the authors refer to the works from Nishimura [5] and Dembart and Yip [20] for a detailed discussion on the topic. To overcome this drawback, the lowfrequency formulation is applied to the high levels of refinement with small local Helmholtz numbers.…”

Section: Multilevel Fast Multipole Methodsmentioning

confidence: 99%

Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

Wolf

Lele

2010

AIAA Journal

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The calculation of acoustic field solutions due to aeroacoustic sources is performed for a large number of observer locations. Sound generation by vortex shedding is computed by a hybrid method and an accurate two-dimensional direct calculation, and the results are compared. The hybrid approach uses direct calculation for near-field source computations and the Ffowcs-Williams-Hawkings equation as the acoustic analogy formulation. The integrations of surface dipole and volume quadrupole source terms appearing in the Ffowcs-Williams-Hawkings formulation are accelerated by a wideband multilevel adaptive fast multipole method. The wideband multilevel adaptive fast multipole method presented here applies a plane-wave expansion formulation for calculations in the high-frequency regime and a partial-wave expansion formulation in the low-frequency regime. The method is described in detail for the solution of a two-dimensional Green's function that incorporates convective effects. The method presented in this work is applied to two-dimensional calculations. However, it can be easily extended to three-dimensional calculations of surface monopole and dipole source terms and volume quadrupole source terms.

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“…The BC basis functions can be presented as linear combinations of RWGs defined on barycentrically refined triangular meshes. Combined with CMP, FDMA is stable at low frequency and the box size of finest level can be set smaller than 0.2k (k stands for the wavelength) without suffering from ''subwavelength breakdown'' [25].…”

Section: Introductionmentioning

confidence: 99%

Fast directional multilevel algorithm combined with Calderon multiplicative preconditioner for stable electromagnetic scattering analysis

Chen

Zhu

Chen

et al. 2010

Micro & Optical Tech Letters

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In this article, a new method called fast directional multilevel algorithm (FDMA) is proposed for three-dimensional electromagnetic problems. Combined with the Caldron identities of Calderon multiplicative preconditioner (CMP), the new algorithm has a fast convergence rate of iterative solvers and is stable at low frequency for the electrical field integral equation solutions. Like the fast multipole method, octree structure is used in our proposed algorithm. However, the new algorithm does not require the implementation of multipole expansions of the Green's function but based only on kernel evaluations. It does not suffer from low-frequency breakdown when the discretization density is high. The numerical results demonstrate that the CMPpreconditioned FDMA leads to significant reduction of both the iteration number and the computer processing use (CPU) time for radar cross section (RCS) calculation.

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The accuracy of fast multipole methods for Maxwell's equations

Cited by 59 publications

References 6 publications

The discrete dipole approximation: An overview and recent developments

The discrete dipole approximation: An overview and recent developments

Acoustic Analogy Formulations Accelerated by Fast Multipole Method for Two-Dimensional Aeroacoustic Problems

Fast directional multilevel algorithm combined with Calderon multiplicative preconditioner for stable electromagnetic scattering analysis

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