High-resolution community earth system model (CESM) plays a crucial role in studying climate complexity and predicting future climate change trends. In the parallel ocean program (POP) component of CESM, the communication overhead of the preconditioned conjugate gradient (PCG) method used in the barotropic mode is the main bottleneck affecting POP2 performance. In the high-resolution (0.1 \(^{\circ }\) ) PCG barotropic solver simulation experiments, as the number of processors increases, the proportion of time spent on global reduction operations gradually increases. To address this issue, we have significantly improved two new barotropic solvers: the preconditioned pipelined conjugate gradient (PIPEPCG) and the preconditioned pipelined conjugate residual (PIPEPCR). The PIPEPCG and PIPEPCR algorithms are based on the PCG algorithm and utilize pipeline technology to reorder the algorithmic process, thereby creating conditions for implementing optimizations such as merging inner product operations and overlapping communication with computation. In these algorithms, we perform inner product merging to execute only one global reduction operation per iteration. Additionally, we replaced the original blocking global reduction functions with non-blocking global reduction, allowing these operations to overlap with matrix–vector multiplication, boundary update operations, and preconditioning operations. We also optimized the position of boundary updates and employed techniques such as residual replacement operations and vector merging to further enhance algorithm performance. Additionally, we replaced the original diagonal preconditioner with an EVP (error vector propagation) preconditioner, which further improved the parallel performance of the algorithm. Our experimental results show that in high-resolution POP2 simulations using 10,000 processors, the new PIPEPCG and PIPEPCR solvers achieved speedup ratios of approximately 1.98x and 1.89x, respectively, compared to the classical PCG solver.
