Sparse approximate inverse preconditioners for iterative solvers on GPUs

Abstract

Iterative solvers with preconditioners are typically employed for the solution of large systems of linear equations. However, the design of preconditioners for the black-box case, in which no additional information about the underlying problem is known, is very difficult. The most commonly employed method of incomplete LU factorizations is a serial algorithm and thus not well suited for the massively parallel computing architecture of GPUs. We investigate sparse approximate inverse preconditioners in this work, which show a very high degree of parallelism. The preconditioner setup is accomplished in a hybrid manner, where parts of the algorithm which require dynamic memory allocations are carried out on the CPU, while the GPU is used for the computationally expensive factorizations. Our benchmark results demonstrate that our implementations in ViennaCL are well suited as a black-box preconditioner for multi- and many-core architectures.