Conjugate gradient method with graphics processing unit acceleration: CUDA vs OpenCL

Performance computations depend on the machine architecture, the operating system, the problem studied and obviously on the programming implementation. Solving partial differential equations by numerical methods such as the finite element method requires the solution of large sparse linear systems. Graphics processing unit (GPU) is now commonly used to accelerate numerical simulations and most supercomputers provide large number of GPUs to their users. This paper proposes a comparison of both CUDA and OpenCL GPU languages to take the highest performance of multi-GPUs clusters. We analyse, evaluate and compare their respective performances for computing linear algebra operations and for solving large sparse linear systems with the conjugate gradient iterative method on multi-GPUs clusters.