An efficient GPU-based fractional-step domain decomposition scheme for the reaction–diffusion equation

Abstract

In the present study, an efficient GPU-based corrected explicit–implicit domain decomposition scheme is proposed to accelerate fractional steps solvers. Implicit time advancement in fractional steps solvers leads to several independent tri-diagonal systems. In the present method, by decomposing the domain and predicting the solution at the interface points, the original tri-diagonal systems are decomposed to several independent systems; this allows partitioning the workloads. After solving the systems, correction is performed to stabilize the solution. The method is implemented using different strategies and memory coalescing, and cache throttling techniques are employed to improve the performance. Numerical experiments are conducted for two- and three-dimensional reaction–diffusion problems to measure the accuracy, stability, and efficiency of the method. The new efficient prediction and correction schemes presented in this study preserve the accuracy and the stability of the solver even for a large number of sub-domains. Therefore, the method provides many independent tri-diagonal systems and creates a large number of threads to keep the GPU occupied. The partitioning procedure is well adapted for GPU-computing; thus, the method effectively accelerates the solution and outperforms the previous methods in terms of computational time.