GPU computing with Kaczmarz’s and other iterative algorithms for linear systems

Elble, Joseph M.; Sahinidis, Nikolaos V.; Vouzis, Panagiotis D.

doi:10.1016/j.parco.2009.12.003

Cited by 63 publications

(35 citation statements)

References 19 publications

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“…These iterative algorithms are distributed by averaging the boundary information, e.g., component averaging (CAV) (Censor et al, 2001) and component averaged row projections (CARP) (Gordon and Gordon, 2005). A survey paper comparing various block parallel methods based on their performance on GPU's is (Elble et al, 2010). Kamath et al (2013) proposed an algorithm called component average distributed multi-resolution evolving tomography (CA-DMET) which involved modification of component average type algorithms such as CAV and CARP for seismic tomography.…”

Section: Related Workmentioning

confidence: 99%

Distributed tomography with adaptive mesh refinement in sensor networks

Kamath

Shi

Chow

et al. 2017

IJSNET

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Existing seismic instrumentation systems do not yet have the capability to recover the physical dynamics with sufficient resolution in real time. Currently, seismologists use centralised tomography inversion algorithm, which requires manual data gathering from each station and months to generate tomography. To address these issues a distributed approach is required which can avoid data collection from large number of sensors and perform in-network imaging to real-time tomography. In this paper, we present a distributed adaptive mesh refinement (AMR) solution to invert seismic tomography over large dense network, which avoids centralised computation and expensive data collection. Our approach first discretises the data and filters them using adaptive mesh to make it well-conditioned. The system is implemented and evaluated using a CORE emulator and we show that the filtered well-conditioned system has lower dimension and improved convergence rate than the original system, thereby decreasing the communication overhead over the network.Keywords: distributed sensing; adaptive mesh; seismic tomography; sensor network; in-network computing.Reference to this paper should be made as follows: Kamath, G., Shi, L., Chow, E. and Song, W-Z. Copyright © 2017 Inderscience Enterprises Ltd. Distributed tomography with adaptive mesh refinement in sensor networks 41Wen-Zhan Song is a Professor in Georgia State University. His research mainly focuses on sensor web, smart grid and smart environment where sensing, computing, communication and control play a critical role and need a transformative study. His research has received 6 million+ research funding from NSF, NASA, USGS, Boeing and etc since 2005, and resulted in 80+ journal papers, conference papers and book chapters in this area. This paper is a revised and expanded version of a paper entitled 'Component-average based distributed seismic tomography in sensor networks' presented at

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Section: Related Workmentioning

confidence: 99%

Distributed tomography with adaptive mesh refinement in sensor networks

Kamath

Shi

Chow

et al. 2017

IJSNET

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“…However, its shared memory implementation requires the duplication of certain nodes in the interior of the MPI partition. Such an approach was pursued in [44] for GPUs, but with moderate success. We will show in Section 5 that the increase in "averaged" vector entries leads to a significant memory overhead in weak and strong scaling experiments with CARP, so that fewer nodes can be used compared to the hybrid approach.…”

Section: Hybrid-parallel Approachmentioning

confidence: 99%

On the parallel iterative solution of linear systems arising in the FEAST algorithm for computing inner eigenvalues

et al. 2015

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a b s t r a c tMethods for the solution of sparse eigenvalue problems that are based on spectral projectors and contour integration have recently attracted more and more attention. Such methods require the solution of many shifted sparse linear systems of full size. In most of the literature concerning these eigenvalue solvers, only few words are said on the solution of the linear systems, but they turn out to be very hard to solve by iterative linear solvers in practice. In this work we identify a row projection method for the solution of the inner linear systems encountered in the FEAST algorithm and introduce a novel hybrid parallel and fully iterative implementation of the eigenvalue solver. Our approach ultimately aims at achieving extreme parallelism by exploiting the algorithm's potential on several levels. We present numerical examples where graphene modeling is one of the target applications. In this application, several hundred or even thousands of eigenvalues from the interior of the spectrum are required, which is a big challenge for state-of-the-art numerical methods.

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“…Its main advantages are robustness and cyclic convergence on inconsistent systems. The block parallel versions of ART have been studied and the comparison of various methods based on their performance on graphics processing units is discussed in Elble, Sahinidis, and Vouzis (2010). Among them, Cimmino's method (Cimmino, 1938) was the first one to introduce a parallel version of ART that guaranteed convergence even in case of inconsistent-system.…”

Section: Distributed Tomography Algorithmsmentioning

confidence: 99%