MLFMA-FFT Parallel Algorithm for the Solution of Extremely Large Problems in Electromagnetics

Taboada, J. M.; Araújo, M. G.; Basteiro, Fernando Obelleiro; Rodríguez, J.L.; Landesa, L.

doi:10.1109/jproc.2012.2194269

Cited by 56 publications

(42 citation statements)

References 24 publications

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“…The parallelization within each task is attained using OpenMP, which exploits the fast memory access in the shared-memory multi-core processors. Finally, we remark that, for a very large number of subdomains, a highly scalable parallel performance in radiation coupling can be achieved by a hybrid MLFMA-FFT algorithm, which has been demonstrated in [53,54].…”

Section: Radiation Coupling Among Subdomainsmentioning

confidence: 83%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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Abstract-This work investigates an adaptive, parallel and scalable integral equation solver for very large-scale electromagnetic modeling and simulation. A complicated surface model is decomposed into a collection of components, all of which are discretized independently and concurrently using a discontinuous Galerkin boundary element method. An additive Schwarz domain decomposition method is proposed next for the efficient and robust solution of linear systems resulting from discontinuous Galerkin discretizations. The work leads to a rapidly-convergent integral equation solver that is scalable for large multi-scale objects. Furthermore, it serves as a basis for parallel and scalable computational algorithms to reduce the time complexity via advanced distributed computing systems. Numerical experiments are performed on large computer clusters to characterize the performance of the proposed method. Finally, the capability and benefits of the resulting algorithms are exploited and illustrated through different types of real-world applications on high performance computing systems.

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Section: Radiation Coupling Among Subdomainsmentioning

confidence: 83%

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

MacKie-Mason¹,

Greenwood²,

Peng³

2015

PIER

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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%

“…The convolution is accelerated in the transformed domain by applying the FFT. By so doing, the workload can be distributed among parallel processes by plane wave samples almost without inter-process communication or synchronization (note that the FFT is never parallelized [32]). A schematic description of this method is shown in Fig.…”

Section: Acceleration Techniquesmentioning

confidence: 99%

“…6(a). As an indication of its power, the MLFMA-FFT method has been used to solve an electromagnetic problem with 1 billion unknowns in 2010 [32], and more recently some applications of this methodology to the field of nanoplasmonics can be found in [22]. However, we can still take a step further when dealing with nanoplasmonic applications.…”

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

Self Cite

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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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ℌ 2 $$\mathcal{H}^{2}$$ Matrix and Integral Equation for Electromagnetic Scattering by a Perfectly Conducting Object

Stavtsev

2017

Integral Methods in Science and Engineering, Volume 2

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MLFMA-FFT Parallel Algorithm for the Solution of Extremely Large Problems in Electromagnetics

Cited by 56 publications

References 24 publications

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

ADAPTIVE AND PARALLEL SURFACE INTEGRAL EQUATION SOLVERS FOR VERY LARGE-SCALE ELECTROMAGNETIC MODELING AND SIMULATION (Invited Paper)

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

ℌ 2 $$\mathcal{H}^{2}$$ Matrix and Integral Equation for Electromagnetic Scattering by a Perfectly Conducting Object

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