High Performance Implementation of Conjugate Gradient Method Using OpenCL on Graphics Processing Units

Most solution methods for Partial Differential Equations (PDEs) find their unknowns through solving a linear system of equations. This step consumes a considerable part of total solution time, and hence accelerating the solution of linear systems of equations has been the subject of many researches. In this research we solve linear systems of equations on Graphics Processing Units (GPUs) using a tunable Sparse Matrix-Vector multiplication (SpMV) implemented in Open Computing Language (OpenCL). We use the Conjugate Gradient (CG) method to this end. Kernel parameters are set such that the linear system of equation is solved in the fastest way possible. For a better performance, two variants of CG which most comply the execution model in OpenCL are implemented and their performances are compared with ViennaCL library on CPU and GPU. In both variants, the kernels are fused to reduce the kernel launch overhead. The results show that the proposed method consistently outperforms the ViennaCL library on a wide range of test systems and problems.