Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems

Waltz, Caleb; Sertel, Kubilay; Carr, Michael; Usner, B.C.; Volakis, John L.

doi:10.1109/tap.2007.898511

Cited by 46 publications

(38 citation statements)

References 22 publications

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“…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. The FFT extension of the latter (MLFMA-FFT) combines the algorithmic efficiency of MLFMA with the high scalability of FMM-FFT [55] via parallelization, which is optimal when using distributed multicore computer clusters. In MLFMA-FFT the translation stage at the top (coarsest) level of the multilevel Cartesian octree decomposition of the geometry is addressed in terms of a 3D circular convolution per sample of the plane wave expansion (Ewald sphere).…”

Section: Acceleration Techniquesmentioning

confidence: 99%

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%

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

Solís¹,

Taboada²,

Landesa³

et al. 2015

PIER

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“…Algorithms with a lower computational complexity are usually more complex and their actual runtime can be dominated by fairly large prefactors. For example, the FFT-MLFMA algorithm has a higher computational complexity than the MLFMA [21], [22]. Nevertheless, the parallelization of the FFT-MLFMA algorithm is highly efficient (in a strong scaling sense) for current cluster sizes.…”

Section: Weak Scaling Analysis: Numerical Validationmentioning

confidence: 99%

Weak Scalability Analysis of the Distributed-Memory Parallel MLFMA

Michiels

Fostier

Bogaert

et al. 2013

IEEE Trans. Antennas Propagat.

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Abstract-Distributed-memory parallelization of the Multilevel Fast Multipole Algorithm (MLFMA) relies on the partitioning of the internal data structures of the MLFMA among the local memories of networked machines. For three existing data partitioning schemes (spatial, hybrid and hierarchical partitioning), the weak scalability, i.e. the asymptotic behavior for proportionally increasing problem size and number of parallel processes, is analyzed. It is demonstrated that none of these schemes are weakly scalable. A non-trivial change to the hierarchical scheme is proposed, yielding a parallel MLFMA that does exhibit weak scalability. It is shown that, even for modest problem sizes and a modest number of parallel processes, the memory requirements of the proposed scheme are already significantly lower, compared to existing schemes. Additionally, the proposed scheme is used to perform full-wave simulations of a canonical example, where the number of unknowns and CPU-cores are proportionally increased up to more than 200 millions of unknowns and 1024 CPU-cores. The time per matrix-vector multiplication for an increasing number of unknowns and CPU-cores corresponds very well to the theoretical time complexity.

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“…As it is shown in [14,15], the FFT extension of the conventional FMM method allows to obtain a great reduction of the MVP CPU time with respect to the FMM. The method consists of employing the Fast Fourier Transform to speedup the translation stage in the framework of the FMM.…”

Section: Fmm-fft Algorithmmentioning

confidence: 99%

“…This variation of the single-level FMM was first proposed in [14] as an acceleration technique applied to almost planar surfaces. Later on, a parallelized implementation was applied to general three-dimensional geometries [15]. The method uses the FFT to speedup the translation stage resulting in a dramatic reduction of the matrix-vector product (MVP) time requirement with respect to the FMM.…”

Section: Introductionmentioning

confidence: 99%

Supercomputer Aware Approach for the Solution of Challenging Electromagnetic Problems

Araújo¹,

Taboada²,

Obelleiro³

et al. 2010

PIER

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Abstract-It is a proven fact that The Fast Fourier Transform (FFT) extension of the conventional Fast Multipole Method (FMM) reduces the matrix vector product (MVP) complexity and preserves the propensity for parallel scaling of the single level FMM. In this paper, an efficient parallel strategy of a nested variation of the FMM-FFT algorithm that reduces the memory requirements is presented. The solution provided by this parallel implementation for a challenging problem with more than 0.5 billion unknowns has constituted the world record in computational electromagnetics (CEM) at the beginning of 2009.

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Massively Parallel Fast Multipole Method Solutions of Large Electromagnetic Scattering Problems

Cited by 46 publications

References 22 publications

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

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

Weak Scalability Analysis of the Distributed-Memory Parallel MLFMA

Supercomputer Aware Approach for the Solution of Challenging Electromagnetic Problems

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