Preconditioners for Batched Iterative Linear Solvers on GPUs

Batched iterative solvers can be an attractive alternative to batched direct solvers if the linear systems allow for fast convergence. In non-batched settings, iterative solvers are often enhanced with sophisticated preconditioners to improve convergence. In this paper, we develop preconditioners for batched iterative solvers that improve the iterative solver convergence without incurring detrimental resource overhead and preserving much of the iterative solver flexibility. We detail the design and implementation considerations, present a user-friendly interface to the batched preconditioners, and demonstrate the convergence and runtime benefits over non-preconditioned batched iterative solvers on state-of-the-art GPUs for a variety of benchmark problems from finite difference stencil matrices, the Suitesparse matrix collection and a computational chemistry application.