Extending Sparse Patterns to Improve Inverse Preconditioning on GPU Architectures

Graphic Processing Units (GPUs) have become a key component of high-end computing infrastructures due to their massively parallel architecture, which delivers large floating-point operations per cycle rates. Many scientific workloads benefit from GPUs and, in particular, numerical methods solving linear systems of equations Ax = b typically run on GPUs. Among them, the Conjugate Gradient (CG) method, which targets linear systems with Symmetric and Positive Definite (SPD) matrices, runs on GPUs using its preconditioned form. However, state-of-the-art preconditioning techniques like the Factorized Sparse Approximate Inverse (FSAI) preconditioner ignore the benefits of data coalescence and locality on GPU architectures and leave substantial performance on the table. These approaches are exclusively based on numerical criteria.