Toward an Automatic Load Balanced Distribution Model in Conjugate Gradient Method for One-Dimensional One-Phase Oil Reservoir Simulation

Abstract

Oil reservoir simulators depend on numerical solvers to solve reservoir algebraic equations which represent the reservoir characteristics. Conjugate Gradient (CG) method is one of the most popular iterative linear solvers used. Parallelizing CG is then an essential step to increase the performance of the simulator using it. In this paper, we introduce an automatic parallel computational loading balancing model for CG. In particular, we introduce an automatic parallel load balanced distributed computational model for the matrix-vector multiplication which heavily contributes to the reduction of the complexity of the CG. Our algorithm allows an equal distribution of the CG computation on the number of workers involved in the parallel computing.