Parallel Orthomin Equation Solver on the Cell Broadband Engine

This paper presents our parallelization and implementation of the ORTHOMIN solver on the Cell Broadband Engine. The solution of linear systems of equation sis 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 PowerPCprocessor element (PPE), and the parallelization and performance analysis of ORTHOMIN across 8 SPEs forTridiagonal (1-D reservoir grid) and Heptadiagonal (3-Dreservoir grid) matrices. Our implementation is shown to scale well with data size, and grid dimensionality.