Utilizing batched solver ideas for efficient solution of non-batched linear systems

The techniques used in batched methods have shown great promise in reducing latency, increasing the memory throughput and maximizing the occupancy of the GPU. In this paper, we adapt these techniques to solve monolithic linear systems and showcase their advantages. We implement this in our production-ready software library, Ginkgo
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and analyze the performance of batched and non-batched iterative solvers on two generations of AMD and NVIDIA GPUs and for AMD and Intel multi-core CPUs. We demonstrate that for relatively small problem sizes, utilizing these techniques for monolithic problems can provide significant performance advantages.