Preconditioned Block‐Iterative Methods on GPUs

Abstract

AbstractAn implementation of the incomplete‐LU/Cholesky preconditioned block‐iterative methods on the Graphics Processing Units (GPUs) using the CUDA parallel programming model is presented. In particular, we focus on the tradeoffs associated with the sparse matrix‐vector multiplication with multiple vectors, sparse triangular solve with multiple right‐hand‐sides (rhs) as well as incomplete factorization with 0 fill‐in. We use these building blocks to implement the block‐CG and BiCGStab iterative methods for the symmetric positive definite (s.p.d.) and nonsymmetric linear systems, respectively. Also, in our numerical experiments we show that the implementation of the preconditioned block‐iterative methods using the CUSPARSE library on the GPU achieves an average of 3× speedup over their MKL implementation on the CPU. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)