Developing an alternating direction explicit-implicit domain-decomposition approach to solve heat transfer equation on graphics processing unit

Document Type : Research Article

Authors

1 Department of Mechanical Engineering, University of Birjand

2 University of Birjand

3 University of Tehran

Abstract

In the present study, a new alternating direction explicit-implicit domain decomposition approach is proposed by combining the alternating direction implicit method with the explicit-implicit domain decomposition method. The method is used for solving the two-dimensional conduction heat transfer equation on a graphics processing unit. In this method, an explicit numerical scheme is used to predict values at the inner boundaries, and an implicit scheme based on the alternating direction implicit method is used to solve the sub-domains. Then, an implicit scheme is used to correct the values on the inner boundaries. Numerical experiments are done to investigate the accuracy and speed of the method. The results show that the present method can achieve a speedup of 1.3 to 2.6 times compared to the alternating direction implicit method. Increasing the number of subdomains increases the speed and decreases the accuracy of the method. Although numerical experiments show high stability of the present method, its error is higher than the alternating direction implicit method. Furthermore, the results show that the present method is more advantageous to problems with coarse grids, such that by increasing the grid size from 256 × 256 to 512 × 512, the speedup decreases from 2.4 to 1.7.

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References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 3 (Special Issue)
June 2021
Pages 1915-1936

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