Developing the new ADI-CEIDD approach to solve the two-dimensional heat transfer equation on GPU

In the present study, the new ADI-CEIDD approach is proposed by combining the ADI method with the explicit-implicit domain decomposition method. The method is used for solving the two-dimensional conduction heat transfer equation on GPU .In this method, an explicit numerical scheme is used to predict values at inner boundaries and an implicit scheme based on the ADI method is used to solve the sub-domains. Then, an implicit scheme is used to correct the values on the inner boundary. The present method increases the number of independent sets of equations and enables more threads to occupy the device. Numerical experiments are done to investigate the accuracy and speed of the method. The results show that the ADI-CEIDD can achieve a speedup of 1.3 to 2.6 times compared to the ADI method. By increasing the number of subdomains from 2 to 32, the speed of the proposed method is increased up to 1.6 times and the accuracy decreases. Although the error of the presented method is higher than the ADI method, numerical experiments show high stability of the ADI-CEIDD. Furthermore, the results show that the ADI-CEIDD method is more advantageous to problems with coarse grid. By increasing the grid size from 256 * 256 to 512 * 512, the value of the Sp decreases from 2.4 to 1.7.