A domain decomposition approach to accelerate the ADI solver on GPU

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

Keywords:

CFD , HPC , CEIDD , GPU , CUDA , domain decomposition , 2D heat conduction equation.