Parallel algorithms on the cedar system

Berry, Michael W.; Gallivan, Kyle A.; Harrod, William J.; Jalby, William; Lo, Sy-Shin; Meier, Ulrike; Philippe, Bernard; Sameh, Ahmed

doi:10.1007/3-540-16811-7_150

Cited by 20 publications

(10 citation statements)

References 11 publications

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“…In a recent publication [1], we have introduced new features of the SPIKE scheme whose main idea dates back to 1977 [2][3][4][5][6][7][8][9][10]. In particular, we consider two new features: (a) a recursive version of SPIKE for handling the reduced system: and (b) effective schemes for exploiting the decay of the elements of the inverse of banded matrices as we move away from the main diagonal.…”

Section: Domain Decomposition Techniques and Parallel Computingmentioning

confidence: 99%

SPIKE: A parallel environment for solving banded linear systems

Polizzi

Sameh

2007

Computers & Fluids

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Section: Domain Decomposition Techniques and Parallel Computingmentioning

confidence: 99%

SPIKE: A parallel environment for solving banded linear systems

Polizzi

Sameh

2007

Computers & Fluids

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“…In this report, we describe important algorithmic and performance-related aspects of Spike, [9,10,33,51,65,66,67,68,70]. The underlying basis for Spike is a divide and conquer technique, which involves the following stages: (a) pre-processing: (i) partitioning of the original system on different processors, or different Symmetric Multiprocessors (SMP's), (ii) factorization of each diagonal block and extraction of a reduced system of much smaller size; (b) post-processing: (iii) solving the reduced system, and (iv) retrieving the overall solution.…”

Section: Introductionmentioning

confidence: 99%

Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures

Grama¹,

Manguoğlu²,

Koyutürk³

et al. 2008

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This report is published in the interest of scientific and technical information exchange, and its publication does not constitute the Government's approval or disapproval of its ideas or findings. OMB No. 0704-0188Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to

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“…In this context block algorithms have been very successful for matrix computations [Berry et al 1986;Dongarra et al 1986;Gallivan 1987;Schreiber 1988]. By considering the matrix at the highest level of the algorithm as a collection of submatrices (the so-called "blocks"), one can express the algorithm in terms of operations such as matrixmatrix multiplication that inherently allow for a great amount of data reuse.…”

Section: Introductionmentioning

confidence: 99%

Adaptive blocking in the QR factorization

Bischof

1989

J Supercomput

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On most high-performance architectures, data movement is slow compared to floating point (in particular, vector) performance. On these architectures block algorithms have been successful for matrix computations. By considering a matrix as a collection of submatrices (the so-called blocks), one naturally arrives at algorithms that require little data movement. The optimal blocking strategy, however, depends on the computing environment and on the problem parameters. On parallel machines, tradeoffs between individual floating point performance and overall system performance also come into play. Current approaches use fixed-width blocking strategies which are not optimal. This paper presents an adaptive blocking methodology for determining a good blocking strategy systematically. We demonstrate this technique on a block QR factorization routine on a distributed-memory machine. Using timing models for the high-level kernels of the algorithm, we can formulate in a recurrence relation a blocking strategy that avoids adding extra delays along the critical path of the algorithm. This recurrence relation predicts performance well since we base our timing models on observed data, not other simplistic measures. Experiments on the Intel iPSC/1 hypercube show that, in fact, the resulting blocking strategy is as good as any fixed-width blocking strategy, independent of problem size and the number of processors employed. So while we do not know the optimum fixed-width blocking strategy unless we rerun the same problem several times, adaptive blocking provides close to optimum performance in the first run. We also mention how adaptive blocking can result in performance portable code by automating the generation of the timing models.

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Parallel algorithms on the cedar system

Cited by 20 publications

References 11 publications

SPIKE: A parallel environment for solving banded linear systems

SPIKE: A parallel environment for solving banded linear systems

Evaluating Sparse Linear System Solvers on Scalable Parallel Architectures

Adaptive blocking in the QR factorization

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