GPU-based parallel algorithms for sparse nonlinear systems

In this work we describe some parallel algorithms for solving nonlinear systems using CUDA (Compute Unified Device Architecture) over a GPU (Graphics Processing Unit). The proposed algorithms are based on both the Fletcher–Reeves version of the nonlinear conjugate gradient method and a polynomial preconditioner type based on block two-stage methods. Several strategies of parallelization and different storage formats for sparse matrices are discussed. The reported numerical experiments analyze the behavior of these algorithms working in a fine grain parallel environment compared with a thread-based environment.

► We propose parallel algorithms for nonlinear systems using CUDA over a GPU.
► Several strategies of parallelization and storage formats are discussed.
► A multicore OpenMP model, a GPGPU model and a mixed model are analyzed.
► The use of CUBLAS and CUSPARSE libraries offer a good performance.
► The use of GPU improves the results obtained using any of the proposed methods.