*Article* **GPU-Based Cellular Automata Model for Multi-Orient Dendrite Growth and the Application on Binary Alloy**

**Jingjing Wang, Hongji Meng \*, Jian Yang and Zhi Xie**

School of Information Science and Engineering, Northeastern University, Shenyang 110819, China **\*** Correspondence: menghonhji@ise.neu.edu.cn

**Abstract:** To simulate dendrite growth with different orientations more efficiently, a high-performance cellular automata (CA) model based on heterogenous central processing unit (CPU)+ graphics processing unit (GPU) architecture has been proposed in this paper. Firstly, the decentered square algorithm (DCSA) is used to simulate the morphology of dendrite with different orientations. Secondly, parallel algorithms are proposed to take full advantage of many cores by maximizing computational parallelism. Thirdly, in order to further improve the calculation efficiency, the task scheduling scheme using multi-stream is designed to solve the waiting problem among independent tasks, improving task parallelism. Then, the present model was validated by comparing its steady dendrite tip velocity with the Lipton–Glicksman–Kurz (LGK) analytical model, which shows great agreement. Finally, it is applied to simulate the dendrite growth of the binary alloy, which proves that the present model can not only simulate the clear dendrite morphology with different orientations and secondary arms, but also show a good agreement with the in situ experiment. In addition, compared with the traditional CPU model, the speedup of this model is up to 158×, which provides a great acceleration.

**Keywords:** GPU-CA model; multi-orient dendrite; parallel algorithm; speedup; task schedule scheme
