Intra-GPU Concurrency in BiCGStab Solvers: Leveraging CUDA Streams for Kernel-Level Parallelism

The Biconjugate Gradient Stabilized (BiCGStab) algorithm is a widely used iterative method for solving large, sparse, and non-symmetric linear systems in scientific and engineering applications. While efficient, its performance is constrained by high iteration costs, memory bandwidth limitations, and synchronization overheads in CPU implementations. This paper investigates GPU-based acceleration of BiCGStab, with particular emphasis on the use of CUDA streams to optimize kernel concurrency and improve resource utilization. A structured hepta-diagonal matrix format is adopted to ensure efficient memory access across both CPU and GPU executions. Performance evaluations are conducted across problem sizes ranging from 1 to 64 million unknowns, comparing single-threaded and multi-threaded CPU baselines against GPU implementations with and without CUDA streams. The results demonstrate that GPU acceleration achieves up to 30× speedup relative to single-threaded CPU execution and up to 5× compared to the best OpenMP configuration (16 threads), with CUDA streams providing an additional 10–20% performance improvement through intra-iteration kernel overlap. Scalability analysis reveals that GPU performance advantages increase with problem size, underscoring the effectiveness of CUDA streams in minimizing idle GPU time and enhancing throughput. These findings highlight the potential of stream-optimized GPU solvers for large-scale scientific simulations and provide a foundation for future extensions incorporating CUDA graphs and multi-GPU environments.