Simulation speed depends on code structures, hence it is crucial how to build a fast algorithm. We solve the Allen-Cahn equation by an explicit finite difference method, so it requires grid calculations implemented by many for-loops in the simulation code. In terms of programming, many for-loops make the simulation speed slow. To solve the problem, we propose a model architecture containing a pad and a convolution operation for the Allen-Cahn equation. Also, the GPU operation is used to boost up the speed more. In this way, the simulation of other differential equations can be improved. In this paper, various numerical simulations are conducted to confirm that the Allen-Cahn equation follows motion by mean curvature and phase separation in two-dimensional and three-dimensional spaces. Finally, we demonstrate that our algorithm is much faster than an unoptimized code and the CPU operation.
翻译：模拟速度取决于代码结构, 因此关键在于如何构建快速算法。 我们用明确的有限差分法解决艾伦- 卡恩方程式, 因此它需要由模拟代码中的许多卢人使用网格计算。 在程序设计方面, 许多卢人使模拟速度缓慢。 为了解决问题, 我们提议了一个包含艾伦- 卡恩方程式的垫子和变速操作的模型结构。 另外, 使用 GPU 操作来提高速度。 这样可以改进其他差异方程式的模拟 。 在本文中, 进行了各种数字模拟, 以确认艾伦- 卡恩方程式在二维和三维空间以中等曲线和阶段分离方式进行运动。 最后, 我们证明我们的算法比未节制代码和 CPU 操作要快得多 。
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