Parallel accelerated cartesian expansions for particle dynamics simulations

Vikram, M.; Baczewzki, A.; Shanker, B.; Aluru, Srinivas

doi:10.1109/ipdps.2009.5161038

Cited by 9 publications

(5 citation statements)

References 18 publications

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“…This is achieved by developing strategies that ensure self-similar distribution of tree data, which leads to an algorithm that is implicitly load balanced. This work extends the recent developments in parallel algorithms for Laplace FMM [23], [29] to the Helmholtz FMM and the resulting algorithm is a seamless combination of spatial and direction partitioning strategies. It is well known, from Amdahl's law, that the maximum parallel speed-up achieved is limited by the minimum time spent on serial computations of an algorithm.…”

Section: Introductionmentioning

confidence: 70%

A Scalable Parallel Wideband MLFMA for Efficient Electromagnetic Simulations on Large Scale Clusters

Melapudi

Shanker

Seal

et al. 2011

IEEE Trans. Antennas Propagat.

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The development of the multilevel fast multipole algorithm (MLFMA) and its multiscale variants have enabled the use of integral equation (IE) based solvers to compute scattering from complicated structures. Development of scalable parallel algorithms, to extend the reach of these solvers, has been a topic of intense research for about a decade. In this paper, we present a new algorithm for parallel implementation of IE solver that is augmented with a wideband MLFMA and scalable on large number of processors. The wideband MLFMA employed here, to handle multiscale problems, is a hybrid combination of the accelerated Cartesian expansion (ACE) and the classical MLFMA. The salient feature of the presented parallel algorithm is that it is implicitly load balanced and exhibits higher performance. This is achieved by developing a strategy to partition the MLFMA tree, and hence the associated computations, in a self-similar fashion among the parallel processors. As detailed in the paper, the algorithm employs both spatial and direction partitioning approaches in a flexible manner to ensure scalable performance. Plethora of results are presented here to exhibit the scalability of this algorithm on 512 and more processors. Index Terms-AcceleratedCartesian expansion (ACE), Cartesian expansions, fast multipole method (FMM), fast solvers, integral equation (IE), multipole methods, parallel multilevel fast multipole algorithm (MLFMA), scattering, self-similar tree, wideband MLFMA.

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Section: Introductionmentioning

confidence: 70%

A Scalable Parallel Wideband MLFMA for Efficient Electromagnetic Simulations on Large Scale Clusters

Melapudi

Shanker

Seal

et al. 2011

IEEE Trans. Antennas Propagat.

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“…FMMs offer an O (N)-complexity and an a priori error estimate, but implementing a fully fledged adaptive FMM in 3D is a daunting task [4]. Parallelization issues complicate matter even further and call for a balance between, on the one hand theoretical efficiency, and on the other hand software complexity [14,16]. A major inconvenience with adaptive versions is the complicated memory access pattern which is due to the communication between levels in the multipole tree.…”

Section: Motivationmentioning

confidence: 99%

On well-separated sets and fast multipole methods

Engblom

2011

Applied Numerical Mathematics

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The notion of well-separated sets is crucial in fast multipole methods as the main idea is to approximate the interaction between such sets via cluster expansions. We revisit the one-parameter multipole acceptance criterion in a general setting and derive a relative error estimate. This analysis benefits asymmetric versions of the method, where the division of the multipole boxes is more liberal than in conventional codes. Such variants offer a particularly elegant implementation with a balanced multipole tree, a feature which might be very favorable on modern computer architectures

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“…Algorithmic strategies abound which restrict the pairwise computations to "neighborhoods," and are important to effectively scale to large problem sizes. For instance, the Fast Multipole Method organizes particles/atoms into a hierarchy of clusters and approximates the field computations at various levels so that pairwise computations are restricted to those between sets of entities in each leaf node, and the entities in spatially neighboring leaf nodes [6]. While we fully assume that such algorithmic strategies should be used whenever available, the runtime is still often dominated by the pairwise computations that are required to be computed.…”

Section: Introductionmentioning

confidence: 99%

Accelerating Pairwise Computations on Cell Processors

Sarje

Żola

Aluru

2011

IEEE Trans. Parallel Distrib. Syst.

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Direct computation of all pairwise distances or interactions is a fundamental problem that arises in many application areas including particle or atomistic simulations, fluid dynamics, computational electromagnetics, materials science, genomics and systems biology, and clustering and data mining. In this paper, we present methods for performing such pairwise computations efficiently in parallel on Cell processors. This problem is particularly challenging on the Cell processor due to the small sized Local Stores of the Synergistic Processing Elements, the main computational cores of the processor. We present techniques for different variants of this problem including those with large number of entities or when the dimensionality of the information per entity is large. We demonstrate our methods in the context of multiple applications drawn from fluid dynamics, materials science and systems biology, and present detailed experimental results. Our software library is an open source and can be readily used by application scientists to accelerate pairwise computations using Cell accelerators.

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Parallel accelerated cartesian expansions for particle dynamics simulations

Cited by 9 publications

References 18 publications

A Scalable Parallel Wideband MLFMA for Efficient Electromagnetic Simulations on Large Scale Clusters

A Scalable Parallel Wideband MLFMA for Efficient Electromagnetic Simulations on Large Scale Clusters

On well-separated sets and fast multipole methods

Accelerating Pairwise Computations on Cell Processors

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