A domain decomposition approach to accelerate the ADI solver on GPU

Abstract

In the present study, a combined method of ADI and CEIDD (ADI-CEIDD) is proposed. In this method, the number of independent tridiagonal systems are more than the ADI method and this allows for more parallelism. Compared with the parallel methods for tridiagonal system of equation the present method does not add any significant overhead to the ADI algorithm and it's easy to implement. The ADI-CEIDD method is implemented on GPU to solve the 2D heat conduction equation. The results show that decomposing the domain in ADI-CEIDD has increased the error compared to the ADI method. Also, the stability of the method is demonstrated. Furthermore, it is observed that the performance of the ADI-CEIDD algorithm is very sensitive to the global memory access pattern, especially in big grid sizes. Also, the results indicated that the ADI-CEIDD outperforms the CR-PCR algorithm at all grid sizes.