Block Epsilon-Circulant Preconditioning with GPU-Accelerated Spatial Solvers for Linear Time-Dependent PDEs
Ryo Yoda, Matthias Bolten · 2025
Parallel implementations and evaluations of parallel-in-time methods for time-dependent partial differential equations often center on CPU environments. It is crucial to keep abreast of the recent advancements in GPU computing, as they can also enhance the performance of parallel-in-time methods. This work focuses on block epsilon-circulant (BEC) preconditioning, a method with promising potential for good convergence and scaling performance among parallel-in-time methods. One of the primary operations of BEC preconditioning is solving space-size complex-valued systems. We implement this operation with GPU computing and investigate its parallel performance. To our knowledge, this is the first study to consider implementing BEC preconditioning using mutiple GPUs. Numerical experiments are used to discuss the selection of the smoother for the spatial multigrid solvers used for the complex-valued systems and demonstrate the strong scaling performance for diffusion and convection-diffusion problems.