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 CPU (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. (C) 2011 Elsevier Inc. All rights reserved.