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From tile algorithm to stripe algorithm: a CUBLAS-based parallel implementation on GPUs of Gauss method for the resolution of extremely large dense linear systems stored on an array of solid state devices

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Abstract

This paper presents an efficient algorithmic approach to the GPU-based parallel resolution of dense linear systems of extremely large size. A formal transformation of the code of Gauss method allows us to develop for matrix calculations the concept of stripe algorithm, as opposed to that of tile algorithm. Our stripe algorithm is based on the partitioning of the linear system’s matrix into stripes of rows and is well suited for efficient implementation on a GPU, using cublasDgemm function of CUBLAS library as the main building block. It is also well adapted to storage of the linear system on an array of solid state devices, the PC memory being used as a cache between the SSDs and the GPU memory. We demonstrate experimentally that our code solves efficiently dense linear systems of size up to 400,000 (160 billion matrix elements) using an NIVDIA C2050 and six 240 GB SSDs.

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Abbreviations

GPU:

Graphical processing unit

CUDA:

Compute unified device architecture

CUBLAS:

CUDA basic linear algebra subroutines

SSD:

Solid state device

L\(_\mathrm{SSD}\) :

1st memory level: array of SSDs

L\(_\mathrm{PC}\) :

2nd memory level: main memory of PC

L\(_\mathrm{GPU}\) :

3rd memory level: global memory of GPU

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  1. Computer Engineering Department, European University of Lefke, via Mersin 10, Gemikonaǧı, Turkey

    Manuel Carcenac

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  1. Manuel Carcenac
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Correspondence to Manuel Carcenac.

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Carcenac, M. From tile algorithm to stripe algorithm: a CUBLAS-based parallel implementation on GPUs of Gauss method for the resolution of extremely large dense linear systems stored on an array of solid state devices. J Supercomput 68, 365–413 (2014). https://doi.org/10.1007/s11227-013-1043-3

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