Mixed-precision implementation of block <i>ϵ</i>-circulant preconditioner on modern CPU-GPU environments

Parallel-in-time methods for time-dependent problems have risen to prominence over the past decade as massively parallel computers push core counts into the millions. Among them, the block ϵ-circulant (BEC) preconditioned solver achieves outstanding convergence, yet the preconditioner itself dominates the solver runtime. We propose a mixed-precision strategy that uses single precision for BEC preconditioning and double precision elsewhere, thereby reducing the solver runtime especially on CPU-GPU systems. On an NVIDIA GH200 cluster, the mixed-precision BEC-GMRES solver achieves a 1.42× speedup for two-dimensional advection-diffusion problems without significant loss of accuracy.