Enhancing Stability and Optimizing Implementation of Mixed-Precision Block epsilon -Circulant Preconditioned Solvers for Parallelization-in-Time

Block epsilon-circulant (BEC) preconditioning achieves excellent convergence for parallel-in-time methods, but GPU implementations face challenges with the efficiency of solvers for complex-valued systems and further with stability when mixed-precision is used to improve performance. We address these limitations through two key innovations: GPU-optimized solvers using AmgX with equivalent formulation of the complex systems and 2 × 2 block CRS storage, and mass-matrix scaling that controls condition number growth in single-precision. The mass-matrix scaling technique reduces condition numbers from 105-106 to below 102, eliminating convergence degradation observed in unscaled FP32 implementations. While FP32 implementations require at least 3 iterations compared to the 2 iterations achieved by FP64 in practice, our analysis reveals that lower precision inner iterations yield faster overall execution times. Performance evaluation on NVIDIA GH200 clusters shows that our optimized block-solver achieves 1.28 × speedup over baseline GPU implementation and strong scaling to 64 GPUs, demonstrating that practical performance benefits.