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Implementation and performance analysis of parallel conjugate gradient on the Cell Broadband Engine

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2 Author(s)
Sibai, F.N. ; Facility of Information Technology, UAE University, Al Ain, United Arab Emirates ; Kidwai, H.K.

This paper presents our implementation of the method of parallel conjugate gradients (CGs) on the Cell Broadband Engine® (Cell/B.E.®). The solution of linear systems of equations is one of the most central-processing-unit-intensive steps in oil reservoir simulation applications and can greatly benefit from the multitude of single-instruction–multiple-data-capable synergistic processor element (SPE) cores in the Cell/B.E. processor. We assume that the linear system of equations is of standard form Ax = B, where A is a square sparse coefficient matrix. Several solvers exist with distinct advantages and disadvantages. When dealing with 1-D, 2-D, and 3-D reservoirs, the resulting coefficient matrix can be formulated as a banded matrix. This paper reports the implementation of the serial CG on the Cell/B.E. PowerPC® processor element (PPE) and the parallelization and performance analysis of CG across 1, 8, and 16 SPEs for tridiagonal (1-D reservoir grid), pentadiagonal (2-D reservoir grid), and heptadiagonal (3-D reservoir grid) matrices. Our implementation is shown to scale well with data size, grid dimensionality, and number of cores.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:54 ,  Issue: 6 )