Parallel Simulation of Oil Reservoirs on a Multi-core Stream Computer

2011 Sixth International Symposium on Parallel Computing in Electrical Engineering

2011

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This paper presents our parallelization and implementation of the ORTHOMIN solver on the Cell Broadband Engine. The solution of linear systems of equations is one of the most central processing unit-intensive steps in many engineering and simulation applications and can greatly benefit from the multitude of SIMD-capable synergistic processor element (SPE) cores in the Cell processor. We report the serial ORTHOMIN implementation on the Cell's PowerPC processor element (PPE), and the parallelization and performance analysis of ORTHOMIN across 8 SPEs for Tridiagonal (1-D reservoir grid) and Heptadiagonal (3-D reservoir grid) matrices. Our implementation is shown to scale well with data size, and grid dimensionality.Parallel linear equation solvers are used in the solution of many engineering and simulation applications. These solvers find the solution of a system of linear equations taking advantage of parallel processing methods. Parallelism is essential to reduce the execution time for large systems of linear equations with thousands of equations and thousands of unknown variables. In prior work [1-2], we parallelized and implemented the Conjugate Gradient solver on the STI (Sony, Toshiba, IBM) Cell Broadband Engine (Cell) platform [8][9][10]. The Cell processor is a multi-core processor with nine cores on a single chip. One core is a PowerPC RISC processor known as the PPE (power processing element). Eight computational cores with vector capabilities are known as the SPEs (synergistic processing elements). With its multi-core parallelism and vector and SIMD processing capabilities, the STI Cell processor was shown to deliver top computation performance levels on graphics and image processing applications [3] and video surveillance applications [4]. Because of the Cell's unique architecture, shorter simulator run times are expected on the Cell platform compared to existing systems. Shorter simulation times translate into faster solutions (in terms of days, depending on the size of the problem) and allow for more simulation runs to be performed on the same hardware resources during fixed time durations.A key component of a simulator in engineering disciplines is a linear equation solver which computes the solution to a system of difference equations. ORTHOMIN is an example of minimal-residual method used in engineering simulations such as oil reservoir simulation. In ORTHOMIN, a series of vectors is generated for x(1), x(2), …, x(k+1) for k+1 <= n starting from an initial estimate of x(0), where n is the number linear equations or the number of unknown variables (unknowns). The linear system equation is of the form A X = B where X is the vector of unknowns, and A and B are scalar vectors. A is known as the coefficient matrix and X is known as the unknown variable matrix. The exact solution is obtained in n iterations assuming no round off errors occur, while an approximate solution is obtained in less than n iterations. The drawback of ORTHOMIN is that it requires a large memory which provides a huge bottleneck on ...

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Section: ) Backgroundmentioning

confidence: 99%

Section: ) Introductionmentioning

confidence: 99%

Parallel Orthomin Equation Solver on the Cell Broadband Engine

2011 Sixth International Symposium on Parallel Computing in Electrical Engineering

2011

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“…In prior work , the Thomas algorithm was used to find an exact solution of the pressure and saturation variables at each grid point of a two‐phase oil/water reservoir. For small grid sizes (32‐128), speedups ranging between two and six were recorded on one Cell BE processor with four and eight SPEs enabled versus the PPE‐only (serial, RISC) implementation.…”

Section: Introductionmentioning

confidence: 99%

Parallelization and performance comparison of the conjugate gradient equation solver on multicore Cell and Xeon computers

Saad

Concurrency and Computation

2011

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SUMMARYMulticore accelerators are used today to supplement traditional superscalar processors in massively parallel computer nodes with extra floating-point computation power. This paper presents our parallelization and performance enhancement and evaluation of the conjugate gradient (CG) linear equation solver with enhanced matrix multiplication on the Cell Broadband Engine accelerator. The paper also compares the CG performance results on the Cell and two CG implementations on a computer with two quadcore Xeon processors, one with OpenMP and the other with OpenMPI. We also report the enhancements made on the CG code and performance analysis of CG on single and dual Cell Broadband Engine packages with 8 and 16 synergistic processing elements and on Xeon for heptadiagonal matrices, in particular to matrix multiplication and synchronization. We also report the communication and computation time breakdowns and the floating point operations per second ratio. Our parallel CG solver is shown to scale well with data size, grid dimensionality, and number of cores.

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

2010

IBM J. Res. & Dev.