GPU Implementation of Iterative Algorithms with Convergence Checks Using C++ Sender/Receiver

This paper proposes a method to implement iterative algorithms with convergence checks using the asynchronous parallel programming model Sender/Receiver, which is scheduled for standardization in C++26. The performance of the proposed method is evaluated using the Himeno Benchmark (himenoBMT). The iterative algorithms considered in this study are those that can be parallelized among the class of algorithms that repeatedly perform computations to obtain a solution until certain predefined conditions are met, including stationary iterative methods such as the Jacobi method. While the original himenoBMT does not include convergence checks and evaluates benchmark performance based on the execution time of a fixed number of Jacobi iterations, this study introduces a GPU implementation of himenoBMT with convergence checks using Sender/Receiver. The benchmark performance of the proposed method is compared with a multicore CPU implementation using OpenMP and a GPU implementation using Standard Parallelism (Stdpar). When using an NVIDIA GeForce RTX 4090 GPU, the proposed method achieved a maximum performance of 969.98 GFLOPS, representing approximately a 62% improvement over the maximum performance of 600.95 GFLOPS achieved by the Stdpar implementation. Furthermore, compared to the execution time of a multicore CPU implementation using OpenMP on a CPU with 16 physical cores and 32 logical cores, the proposed method demonstrated up to a 23.21-fold speedup. Although the asynchronous nature of the proposed method introduces variability in the number of iterations required for convergence, the impact on execution time was found to be small.