hcaPCG: A Heterogeneous and communication-avoid PCG with Jacobi preconditioner on SW26010-Pro architecture

Due to its efficiency and versatility, the preconditioned conjugate gradient algorithm has long been a staple in the realm of iterative linear system solvers. In this paper, we proposed an optimized preconditioned conjugate gradient algorithm tailored for the SW26010-Pro manycore processor, The main work includes: Optimizing data block sizes based on the processor’s storage structure; combining thread-level and data-level parallelism, utilizing manual SIMD to improve efficiency; optimizing the memory access pattern by employing direct memory access and overlapping of computation and communication; employing a shared-memory approach to store long vectors across all cores. Furthermore, we design an accelerated algorithm for reduction operations, to avoid data communication. Experimental results show that the hcaPCG yields up to 28.1× speedups on average compared to the original implementation.